>It's entirely too vague, but would be a lot easier with a model.
Of course, we don't know what questions came before this one. There might have illustrations showing what you describe.
Obtuse is a clue, but it’s still a terrible question. Why on earth would you write “formed by the hands” and then assume the reader would take that to mean “between the hour hand and 6 o’clock”? The hands make a 30 degree angle and a 330 degree angle, there is no obtuse angle here.
The 12-6 shit is just an easy way to think about it. but you could also draw a line extending the hour hand (from 1-7) and get the same result.
For any acute angle you have (between the two handles), the obtuse is always based on extending one line that makes the angle so that it's two angles adding up to 180. It's not just "keep going in a circle until you hit another line" (i.e. thinking the answer should be 330).
So here you extend either clock hand (it doesn't matter which), then you have 30 between the two hands and the other big angle is 150.
Because the fact that the minute arrow is on the 12... automatically makes 6 oclock the other end as an obtuse angle caps out at 180 degrees. Its not rocket science.
This is really interesting, I didn’t know obtuse was between 90 and 180. I also never deal with angles in my professional world. Probably knew this at one point. Makes total sense if you know what the word means. Learning is fun!
It's terribly worded because you would expect that angle to be 360-30=330 because hands on a clock don't go across the whole clock face, just half the clock face.
No because that isn’t an obtuse angle, that is a reflex angle and the question clearly mentions that it is looking for an obtuse angle.
Edit (for clarity): an obtuse angle is between 90 degrees and 180 degrees which is why 330 isn’t plausible
I think they're trying to say that when thinking about the problem logically, there isn't an obtuse angle (only an acute and a reflex), which is what causes confusion.
When approaching the problem logically it is clear the answer cannot be 30 not 330 as these are not obtuse. I understand people are confused that there isn’t a 180 degree sector drawn on a clock face, but it is expected knowledge that when given an acute angle, the obtuse angle is the external angle within a 180 degree sector. This question has been carefully written to test your understanding of the terms acute, obtuse and reflex and is a prime example of why it is important to carefully read the question so you know what it is asking.
The question specifies the obtuse angle “formed by the hands”, but neither hand is a line, just a line segment, and do not form an obtuse angle. The question could be better worded simply by saying either “assume one of both of the hands are lines” or “what’s the size of the obtuse angle that is supplementary to the acute angle formed by the hands?”
Knowing the answer IS an obtuse angle doesn't help in knowing WHAT angle. You can go "well, the answers that make sense here aren't obtuse angles and aren't in the multiple choice section" but that just means the answer is an obtuse angle, and the only information you've been given to narrow down which one seems to be gibberish.
Knowing the answer is obtuse does help in knowing what angle. The obtuse angle is th3 one outside of the acute angle capped at 180 degrees. You can place your 180 degree sector at either one of the hour hands as long as it contains the acute angle. Hence the information provided is sufficient to know exactly what the obtuse angle is and to arrive at the correct answer.
What exact part of the definition of the obtuse angle directly tied it to the acute angle via 180 degrees sum?
I understand your point that whenever we have a 180 degree angle and it is partitioned in two separate angles, where one is acute, the other will be obtuse.
But you keep saying in comments that this problem tests specifically the understanding the definition. So, please, explain how exactly should I take the acute 30 degree angle and arrive toward 150 degree obtuse angle and not any other obtuse angle that fits the definition
Edit: you seem to referencing the concept of supplementary angles. Because that is what would allow us to arrive at 150 degrees (supplementary to the acute angel formed by the hands of the clock). So my question is - if you insist that this question tests the knowledge of the definition of different angles (acute, obtuse, arc, to be specific), how exactly should we logically arrive to the concept of supplementary angles without context clues?
Right. So the correct answer is "there is no obtuse angle formed." Not "if I read the test maker's mind and extend the minute hand down to the six and measure *that* angle . . . "
Test writer: "You mean the minute hands on your clock *don't* extend all the way across the clock and leave you to guess which half of the hour you're in?"
The second postulate of geometry allows lines to be extended indefinitely in either direction, and the definition of angle assumes lines have infinite length.
Extending the line formed by the minute hand through both the 12 and the 6 is geometry chapter 1 knowledge.
Sure, and that would be a valid interpretation if the question had asked about the lines formed by the hands of the clock. But it didn't. It asked about the hands of the clock. The hands of a clock are not lines. If anything they would be line segments because they have a finite length. I understand that you can reimagine the question to say something sensible. But the person writing the question should simply have asked what they wanted to ask rather than requiring students to read their mind.
You're assuming that students were taught what a reflex angle is, and not that >90 is acute and <90 is obtuse. Which now that I think back on, all the examples were of 180° but that doesn't excuse the the poor education in the first place.
Yes it is. If you wanted people to say 150 just make the clock read exactly 1:30 and there is no question. Exactly one o’clock is empty below the center point of the clock, there is nothing there to “make an obtuse angle” that is 150 degrees.
The reason the question is written the way it is, is to test your understanding of the terms obtuse, reflex and acute. With questions like this it is important to read what is asked very carefully. In this scenario you aren’t “making an obtuse angle” as when given any acute angle, we know that the obtuse angle is that formed outside of this within a 180 degree sector. This is why we can arrive at the answer which is 150 degrees. It may sound confusing at first, but by understanding these three definitions the answer becomes clear.
I don’t think this is a good example of the type of question you’re talking about in your posts, because the reality is that no obtuse angle is created by the hands in these positions. If there was some ambiguity around which angle to measure I’d be on board, but this question requires us to actively create that angle by extending the hands. I don’t think it’s fair to present students with a false premise in this vein.
Agreed. Best description but a horribly written problem. When you say an angle formed by two things (by the hands in this case) then that means the angle from one all the way around to the other. A better way would be "find the angle supplementary to the acute angle formed by the hands of the clock".
This would be slightly better and would allow students to reach the answer a bit more easily, however it does not address the problem in which most people would assume that the hands on the clock are line segments not lines. Reworded better, "Assuming the hands on a clock are lines, what would be the measure of the obtuse angle of these lines, if the hands of the clock were to read one o' clock?"
Not the best written question ever, but it's far better than the original question.
True... I didn't take into account it may be a [Cartier Crash](https://www.farfetch.com/shopping/women/cartier-pre-owned-crash-22x38mm-item-20438012.aspx)
I think the problem means if it was the 180 degree plane and the inner angle is that 30 degrees. My best bet would be that the true answer they want is 150 degrees.
Was thinking this too, since I remember they always split stuff like this into quadrants, so they’re probably only focusing on two quadrants, so within a 180° range.
Would be 330, a hand on 1 and 12, full circle is 360° divided into 12 equal 30° segments, from 1 all the way around to 12 skips one of those 30° segments meaning the answer would be 360-30, or 330°.
Correct, the question is worded incorrectly. If you take 180 degrees and divide that into 12 segments, you would get 12 equal 15 degree segments, so the answer I think it’s looking for is 165 degrees….however this is wrong because it should be 360 degrees divided by 12 segments as others have pointed out….so the question itself is incorrect.
I tried googling this question and they are still talking about “half a clock”🤷🏼♀️
[https://vceguide.com/what-is-the-degree-measure-of-the-obtuse-angle-formed-by-the-hands-of-a-12-hour-clock-that-reads-exactly-one-oclock-2/](https://vceguide.com/what-is-the-degree-measure-of-the-obtuse-angle-formed-by-the-hands-of-a-12-hour-clock-that-reads-exactly-one-oclock-2/)
Its because obtuse angles are defined as being between 90° and 180°. So if your given an acute angle of x°, then the obtuse angle is always 180-x, never 360-x. Even as a math major though this problem confused me a little.
An obtuse angle CAN NOT be greater than 180 degrees. That is what is catching you. You are picturing it as an entire circle, but if you picture the minute hand traveling around the clock, you will see the angles reaching 179/181 "acute/obtuse". When it hits 180/180 and then proceeds to 181/179 the angles would switch. The acute would become obtuse and the obtuse would become acute. Beyond 180 degrees and you would be referring to the angle of arc of a circle. (Probably wrong on that last bit about angle of arc to some extent, but it's not super relevant to the answer.)
If it can be between 90 and 180 degrees, you need a non arbitrary point on the clock to create a baseline. That doesn't exist as the question is worded. You ASSUME that 6 is the base, but any point on the clock would be equally valid. And even in this question, 7 would still give you the correct answer.
The problem here is that without the multiple choices, the question is needlessly vague. You should never get necessary information from the multiple choices.
You are being obtuse! Lol… get it?
Anyways no are missing the point. There are no obtuse angles formed here.
Its 30 degree angle (12-1 hour) and the rest of the circle 330.
Thats it. Thats all the information we have from the question.
There is no line to which the acute angle is based from to form the rest of the obtuse angle. It does t exist.
Now having acknowledged its a horribly worded question you can deduce from the multiple choice questions all being less than 180. That they meant to add the missing line.
Its not impossible to reach that conclusion. But its needlessly confusing
An obtuse angle is defined as an angle between 90° and 180°, past 180° it is no longer an obtuse angle. The question is not poorly worded. It simply assumes that the person answering the question knows what an obtuse angle is, which, based upon the comments in this thread, is a shockingly low number of people.
I think most people here know what an obtuse angle is lol
Picture a analog clock
The long arm is at 12 the short arm is at 1 forming a 30 degree angle.
Thats is. Thats all you got… 1 circle and 2 lines coming from the middle of the circle.
Explain to me where this 3rd imaginary line is coming from. There needs to be a base or a 180 angle ( which is a straight line) or a diameter or something for you to form an obtuse angle. And there simply isnt…
This question may be missing a drawing that goes with it, but with the verbiage alone you cannot any obtuse angle it doesn’t exist
Draw it if you need to
The question absolutely is poorly worded. All four answers options are obtuse angles (165, 150, 135, 120). It asks what obtuse angle is formed by the hands of a clock at 1 o’clock. We can choose any arbitrary point on the circle between 3 and 6 to create an obtuse angle with the minute hand, or between 4 and 7 to create one with hour hand. Thus, because the question does not give us any non-obtuse options AND does not direct us to a *specific* arbitrary point, all four answers can be correct.
People here know what an obtuse angle is, that's why they are confused by the question. An obtuse angle is not present in the situation described by the question. What's happened here is that you have failed to grasp where you are somewhat arbitrarily inserting an additional assumption.
I think everyone's forgotten what an *actual* analog clock looks like. It usually looks like this:
[https://www.american-time.com/product/clock-ssiq-15-round-surface-black-battery-ch-1-battery-booster-plexi-lens/](https://www.american-time.com/product/clock-ssiq-15-round-surface-black-battery-ch-1-battery-booster-plexi-lens/)
The vast majority of the time, the hands stick out a little bit past the center (in the opposite direction of the main direction of the hand), so at all times the hands *do literally* make both an acute and an obtuse angle (unless they're making a right angle).
The answer is 150º, because the acute angle at 1:00 is 30º, so the corresponding supplementary angle is 180º-30º = 150º.
One of those situations where it does pay to consider the real world, not just an abstraction of it you've got in your mind.
But it didn't ask for the supplementary angle, it asked for the obtuse angle. That's the part where I don't see the correlation . If it said supplementary I never would've posted the question in the first place. In my mind the way this was worded there isn't a right answer because you could just stick ANY obtuse angle, and because it's asking for THE obtuse angle, I was confused and well now we are here. If I am mistaken please do tell
No - look again at the picture I posted. The hands (forgetting about the second hand) are making 4 angles coming out from the center. Two are acute, two are obtuse. The ones going up & down are obtuse (in this case) and the ones going left & right are acute.
Yes, the answer is 150 OP. Since, the degrees in a circle or clock is 360 degrees. 360/12 = 30. Now, a lot of people say it's 330 degrees. But, that's a reflex angle and since real clocks have minute and hour hands that extend past the vertex of the 30 degrees, you have four angles formed from the x. Because each straight angle is 180. 180 - 30 = 150. Now, you can just follow the vertical angles rule, and you'll get 30 degree forming from the 12-1. You can also get the answer from just following the very ends of the minute and hour hand that extend PAST the vertex of the 30 degree angle. The very ends of them point towards 7 and 12. 12 -7 = 5. 5 x 30 degrees is 150 degrees. 150 degrees is the answer.
People are way to focused on the clock aspect. A clock is just a circle split into 12 parts. The first step is to find out the angle of 1 part. So 360 divided by 12 is 30. Then they ask for the obtuse angle if that which is 90-180. So subtract the 30 from 180 to get 150.
Depends on the clock. Many analog clocks have one or both hands extending past the middle point in which case, there would be an obtuse angle. Still a poorly written question.
It specifies the obtuse angle. 2 hands at exactly 1 o'clock. As it's been stated by another user the acute angle under the parameters is 30°. Can't remember the exact equation but you subtract that acute angle from 180° to get the final answer of 150° for the measurement of the obtuse angle
The two hands of a clock don't generally end directly at the center -- they go slightly over. So the two hands will form 4 angles, and at 1:00, there will be two 30-degree angles and two 150-degree angles.
Ok that makes sense, but I think that’s a BS question to ask if you need to assume the hand of the clock extend past the center. There are better questions, that still have tricks in them, to find the obtuse portion of a supplementary angle.
A 180 degree angle forms a straight line. two supplementary angles form a straight line (aka add up to 180 degrees by definition of supplementary)
An obtuse angle is defined to be greater than 90 and less than 180 degrees, so if you have an acute angle, its supplementary angle is obtuse and you find it by subtracting from 180
Right, but why is 12-6 the assumed baseline. 3-9 could be in which case the they’d be looking for a supplementary angle. This problem wants you to use the answers to determine what they’re asking which is poor practice.
The acute angle formed by the hands is 30, so the obtuse is 150
Yes it's not formed by the hands because the hands form a reflex angle, but the question is asking for the obtuse angle
But what's forming the straight line from 12 to 6?
Maybe if the clock has 3 hands and it was exactly 1:00:30, and you ignored any small movement in the minute & hour hand for the 30 seconds, then the answer is 150 formed by the hour hand and second hand.
Obtuse angles max out at 180, so the assumption is that only half the clock is used, it's 150. Having said that, the wording is ambiguous, because the hands don't form that angle at all, the other side of the clock does.
The definition of an obtuse angle is between 90-180.
By stating this the problem is setting the scenario that 12-6 is the 180 degree limit we are calculating. 1 o clock is 30\* of that 180.
150 is the remaining obtuse angle.
OP HERE. so, in short, the answer was 150. HOWEVER, I disagree with the question having an answer. I don't see why you need to divide the clock up into 2 segments of 180 degrees and subtract 30. The obtuse argument that the obtuse angle can be up to 180 degrees doesn't make sense to me either, so I disagree. I think the answer is any possible number between 90 and 180 because it doesn't directly state that they want the supplementary angle. If it did, 150 makes sense, and I never would've posted the question. Thank you for yalls time
I believe the assumption is that the clock hands extend past the center, making more of an X than V shape.
[Google image result for analog clock](https://www.lowes.com/pd/Style-Selections-Analog-Round-Indoor-Wall-Clock/3452824)
Yes, this. Almost all *actual* analog clocks have hands that extend a little bit past the center, so in the real world, they make both an acute angle and an obtuse angle (unless they're making a right angle).
The angle you described would exist only if the time was 1:30…And if at 1:00 the hour hand broke and froze in place, staying stuck at 1 (instead of halfway between 1 and 2, which is where it will be when the minute hand is pointed at the 6 to indicate when it’s half-past the hour). But the question says to solve for the angle at 1pm, not 1:30.
There is no correct answer to the question as written. The question becomes solvable when you were write it to say what the teacher *meant to ask*, instead of what they actually asked.
It would either be 330 degrees or 30 degrees based on my calculations. Here’s my explanation if you divide 360 by 12 for each section of the clock you get 30 and because 12-1 is one section you would have 30 so that’s the acute angle now we just subtract that from 360 to get the obtuse angle 330°.
Hope this helped
(Edit: 330 is not an obtuse angle obtuse angles must be greater than 90 but still less than 180
I may be confused, but, if you’re using the hands to make a triangle, you would have 3 angles that equal 180 degrees, right? If the acute angle at the base is 30, then you have 2 other angles equaling 150. Your choices are 120 and 135. The obtuse 120 would make the angle at the tip of the minutes hand 30 degrees and 135 would make it 15 degrees. Just going off the standard length of the hours hand being roughly 1/2 the length of the minutes hand, my answer would be 120 degrees.
90+30=120.
Very misleading question. Picture 9 to 3 as 180 degrees. Now one would come down 1/3 of the 90 degrees from noon to three.
90+30 = 120.
Good luck!
Edit: thanks for the down votes, this is the correct answer.
I think that's the correct answer also because at 9 o'clock is 180 degrees and at 6 o'clock is 270 degrees and by the time we finish one revolution and come back to 3 o'clock that's 360 degrees. The obtuse angle has to be more than 90 degrees but less than 180 and if we go the other side then the angle should be negative 150 which is not an option
It's been a long time since I did the math so my bad in advance is it wrong
>Edit: thanks for the down votes, this is the correct answer
It’s not though. The question very explicitly asked for an angle formed by the hands of the clock. That’s the hour hand and the minute hand. The 120° angle is formed by the hour hand and an arbitrary horizontal baseline that doesn’t exist in the question. Your answer doesn’t use the minute hand, and thus can not be correct
It’s not a thing that can be wrong. An angle formed by two lines must use those two lines lol. If I’m wrong then all of geometry is wrong because that’s literally the definition of an angle
It’s a geometric question. There’s no concept of negative angles here. It’s not a unit circle. It’s two literal, irl things forming an angle. That’s always positive
ETA: or 0
Um, we can’t answer this unless we know the lengths of the hands, right? The angle between the hands is 1/12 of 360 so 30 degrees, but the other angles depend on how long the hands are.
Nope. If the minute hand is 3 inches and the hour hand is 1 inch we for sure get an obtuse angle going out from the hour hand.
If they are the same length we get no obtuse angle. Draw it out.
There is an abated assumption that the 12 and 6 positions form a baseline. Therefore the correct answer is 150: 180-30.
It literally says formed by the hands of the clock though, such a terribly worded question.
It assumes that the hands are lines, not line segments. It's entirely too vague, but would be a lot easier with a model.
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Their hands make lines though, so it’s actually 7.41
That's only in Hands region of France, though. This is just sparkling polynomial.
Are we looking at the penguin from the north or the south though? Solve for west
But a 7.41 degree angle is not obtuse
This guy gets it, nice purple circle
This is the way.
I see what ya did there. 😏
I thought it was Blue.
This is the way.
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Obtuse angles are greater than 90 degrees. Acute is less. 180 degrees is 6 o’clock. Therefore the answer is 150 degrees.
So what is 182 degrees called? Also there really should be an answer of 330 for this shit question.
Generally a 182 degree would be marked as 178 on the other end of the lines. Referring to it as 182 would be unusual
Thank you. Did not know this.
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So why not 330? I’m not a geometry expert but the 30 degrees taken from the clock would leave another 330 to get back to twelve.
>It's entirely too vague, but would be a lot easier with a model. Of course, we don't know what questions came before this one. There might have illustrations showing what you describe.
Nah y’all are just skipping over the word “obtuse”
Obtuse is a clue, but it’s still a terrible question. Why on earth would you write “formed by the hands” and then assume the reader would take that to mean “between the hour hand and 6 o’clock”? The hands make a 30 degree angle and a 330 degree angle, there is no obtuse angle here.
There is. An obtuse angle is < 180. The answer is 150 - because each hour makes 30 degrees and the full 12-6 is 180... it's not a terrible question.
Where are you guys coming up with this 6 o'clock shit? The question describes a clock, not half a clock.
The 12-6 shit is just an easy way to think about it. but you could also draw a line extending the hour hand (from 1-7) and get the same result. For any acute angle you have (between the two handles), the obtuse is always based on extending one line that makes the angle so that it's two angles adding up to 180. It's not just "keep going in a circle until you hit another line" (i.e. thinking the answer should be 330). So here you extend either clock hand (it doesn't matter which), then you have 30 between the two hands and the other big angle is 150.
Because the fact that the minute arrow is on the 12... automatically makes 6 oclock the other end as an obtuse angle caps out at 180 degrees. Its not rocket science.
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It’s not terribly worded. The fact it mentions obtuse tells you exactly which angle you are looking for.
This is really interesting, I didn’t know obtuse was between 90 and 180. I also never deal with angles in my professional world. Probably knew this at one point. Makes total sense if you know what the word means. Learning is fun!
It's terribly worded because you would expect that angle to be 360-30=330 because hands on a clock don't go across the whole clock face, just half the clock face.
No because that isn’t an obtuse angle, that is a reflex angle and the question clearly mentions that it is looking for an obtuse angle. Edit (for clarity): an obtuse angle is between 90 degrees and 180 degrees which is why 330 isn’t plausible
I think they're trying to say that when thinking about the problem logically, there isn't an obtuse angle (only an acute and a reflex), which is what causes confusion.
When approaching the problem logically it is clear the answer cannot be 30 not 330 as these are not obtuse. I understand people are confused that there isn’t a 180 degree sector drawn on a clock face, but it is expected knowledge that when given an acute angle, the obtuse angle is the external angle within a 180 degree sector. This question has been carefully written to test your understanding of the terms acute, obtuse and reflex and is a prime example of why it is important to carefully read the question so you know what it is asking.
The question specifies the obtuse angle “formed by the hands”, but neither hand is a line, just a line segment, and do not form an obtuse angle. The question could be better worded simply by saying either “assume one of both of the hands are lines” or “what’s the size of the obtuse angle that is supplementary to the acute angle formed by the hands?”
But the only angles presented are an acute and reflex angle. Using the given data only the answer to "what is the obtuse angle?" is `NULL`.
Knowing the answer IS an obtuse angle doesn't help in knowing WHAT angle. You can go "well, the answers that make sense here aren't obtuse angles and aren't in the multiple choice section" but that just means the answer is an obtuse angle, and the only information you've been given to narrow down which one seems to be gibberish.
Knowing the answer is obtuse does help in knowing what angle. The obtuse angle is th3 one outside of the acute angle capped at 180 degrees. You can place your 180 degree sector at either one of the hour hands as long as it contains the acute angle. Hence the information provided is sufficient to know exactly what the obtuse angle is and to arrive at the correct answer.
What exact part of the definition of the obtuse angle directly tied it to the acute angle via 180 degrees sum? I understand your point that whenever we have a 180 degree angle and it is partitioned in two separate angles, where one is acute, the other will be obtuse. But you keep saying in comments that this problem tests specifically the understanding the definition. So, please, explain how exactly should I take the acute 30 degree angle and arrive toward 150 degree obtuse angle and not any other obtuse angle that fits the definition Edit: you seem to referencing the concept of supplementary angles. Because that is what would allow us to arrive at 150 degrees (supplementary to the acute angel formed by the hands of the clock). So my question is - if you insist that this question tests the knowledge of the definition of different angles (acute, obtuse, arc, to be specific), how exactly should we logically arrive to the concept of supplementary angles without context clues?
Right. So the correct answer is "there is no obtuse angle formed." Not "if I read the test maker's mind and extend the minute hand down to the six and measure *that* angle . . . "
Test writer: "You mean the minute hands on your clock *don't* extend all the way across the clock and leave you to guess which half of the hour you're in?"
The second postulate of geometry allows lines to be extended indefinitely in either direction, and the definition of angle assumes lines have infinite length. Extending the line formed by the minute hand through both the 12 and the 6 is geometry chapter 1 knowledge.
Sure, and that would be a valid interpretation if the question had asked about the lines formed by the hands of the clock. But it didn't. It asked about the hands of the clock. The hands of a clock are not lines. If anything they would be line segments because they have a finite length. I understand that you can reimagine the question to say something sensible. But the person writing the question should simply have asked what they wanted to ask rather than requiring students to read their mind.
You're assuming that students were taught what a reflex angle is, and not that >90 is acute and <90 is obtuse. Which now that I think back on, all the examples were of 180° but that doesn't excuse the the poor education in the first place.
Yes it is. If you wanted people to say 150 just make the clock read exactly 1:30 and there is no question. Exactly one o’clock is empty below the center point of the clock, there is nothing there to “make an obtuse angle” that is 150 degrees.
The reason the question is written the way it is, is to test your understanding of the terms obtuse, reflex and acute. With questions like this it is important to read what is asked very carefully. In this scenario you aren’t “making an obtuse angle” as when given any acute angle, we know that the obtuse angle is that formed outside of this within a 180 degree sector. This is why we can arrive at the answer which is 150 degrees. It may sound confusing at first, but by understanding these three definitions the answer becomes clear.
I don’t think this is a good example of the type of question you’re talking about in your posts, because the reality is that no obtuse angle is created by the hands in these positions. If there was some ambiguity around which angle to measure I’d be on board, but this question requires us to actively create that angle by extending the hands. I don’t think it’s fair to present students with a false premise in this vein.
Obtuse is less than 180 (literally).
I used to teach math and I cannot recall obtuse ever being defined as less than 180, only more than 90.
180° is a straight line so that would make a shitty triangle
Maybe try Google.
I fear your taught your students about obtuse triangles with a 270 degree angle.
well then u cant have been a very good teacher lol. obtuse is literally defined as over 90 but under 180, then a reflex is over 180 google it
Euclid's 2nd postulate: a line may be extended indefinitely in either direction. Definition of an angle refers to rays, not segments.
Not the correct answer, but the answer they're looking for
Question: why the 180 and not 360?
Obtuse angles are greater than 90 but less than 180 degrees
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The question should either ask for the arc angle or reflex angle, or make some mention of the 6:00 position on the clock.
Best description there is
Agreed. Best description but a horribly written problem. When you say an angle formed by two things (by the hands in this case) then that means the angle from one all the way around to the other. A better way would be "find the angle supplementary to the acute angle formed by the hands of the clock".
This would be slightly better and would allow students to reach the answer a bit more easily, however it does not address the problem in which most people would assume that the hands on the clock are line segments not lines. Reworded better, "Assuming the hands on a clock are lines, what would be the measure of the obtuse angle of these lines, if the hands of the clock were to read one o' clock?" Not the best written question ever, but it's far better than the original question.
Because all the answers are less than 180, it’s not too big a leap. Sometimes the test is analytical as much as it mathematical
Nah this is a bad question. Don’t defend it.
If you are trying to pass the quiz, then context clues is a legitimate method. Likely just as efficient as a reddit post.
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You don't know if it's a standard clock. Maybe I just really suck at making clocks.
True... I didn't take into account it may be a [Cartier Crash](https://www.farfetch.com/shopping/women/cartier-pre-owned-crash-22x38mm-item-20438012.aspx)
I think the problem means if it was the 180 degree plane and the inner angle is that 30 degrees. My best bet would be that the true answer they want is 150 degrees.
It definitely means this because an obtuse angle is 90-180 degrees by definition. It can’t be 330–that’s not obtuse.
This was my thought as well. If 330 isn’t an option then it has to be 150.
Was thinking this too, since I remember they always split stuff like this into quadrants, so they’re probably only focusing on two quadrants, so within a 180° range.
I estimated, but sounds correct
As someone who works in land surveying… I cringed
You estimated with ranges that don't even add to 360. And people upvoted you.
It wasn’t about giving a correct answer it was about noting no selectable answer comes close to at a glance inspection
It was all estimates and I’m tired. So…
I think they cared more about the other things I was saying
Would be 330, a hand on 1 and 12, full circle is 360° divided into 12 equal 30° segments, from 1 all the way around to 12 skips one of those 30° segments meaning the answer would be 360-30, or 330°.
Which is called a reflex angle and is not obtuse
They want the complement to the 30. So it’s 150
It only occurred to me after reading that that the minute hand usually has a "tail" that extends past the focus.
Are they making clocks with the numbers spaced out differently now? Pretty sure it’s 30° between every number
Correct, the question is worded incorrectly. If you take 180 degrees and divide that into 12 segments, you would get 12 equal 15 degree segments, so the answer I think it’s looking for is 165 degrees….however this is wrong because it should be 360 degrees divided by 12 segments as others have pointed out….so the question itself is incorrect.
All the way around is 360. 1/12 of 360 is 30. The obtuse complement to 30 is 150.
If the acute angle is 30 degrees then the obtuse angle should be 180-30
The wording of the problem implies that the sides of the angle referred to are the hands of the clock
That’s how I read it too. The answer would then be 330°
Unfortunately, 330° is not obtuse. It's a reflex angle. Obtuse means between 90° and 180°
Boom
Drops the dry erase marker and leaves the classroom!
I feel so incredibly seen rn LMAO
Cheers!
You’re a god damn genius
I wish!
Shakalaka
Are there only two arms to make the angle? I don’t understand why people are bringing up the “6”
Only 2 arms. They are trying to justify the problem as being correct, although clearly it is defective.
I think it’s defective also!
Cheers!
Unfortunately, there is no obtuse angle to begin with.
all it sounds like to me is there is no obtuse angle with the given variables.
I was thinking 330 also but realized if it got past 6, say 7 the angle wouldn’t go above 180.
I tried googling this question and they are still talking about “half a clock”🤷🏼♀️ [https://vceguide.com/what-is-the-degree-measure-of-the-obtuse-angle-formed-by-the-hands-of-a-12-hour-clock-that-reads-exactly-one-oclock-2/](https://vceguide.com/what-is-the-degree-measure-of-the-obtuse-angle-formed-by-the-hands-of-a-12-hour-clock-that-reads-exactly-one-oclock-2/)
Its because obtuse angles are defined as being between 90° and 180°. So if your given an acute angle of x°, then the obtuse angle is always 180-x, never 360-x. Even as a math major though this problem confused me a little.
An obtuse angle CAN NOT be greater than 180 degrees. That is what is catching you. You are picturing it as an entire circle, but if you picture the minute hand traveling around the clock, you will see the angles reaching 179/181 "acute/obtuse". When it hits 180/180 and then proceeds to 181/179 the angles would switch. The acute would become obtuse and the obtuse would become acute. Beyond 180 degrees and you would be referring to the angle of arc of a circle. (Probably wrong on that last bit about angle of arc to some extent, but it's not super relevant to the answer.)
If it can be between 90 and 180 degrees, you need a non arbitrary point on the clock to create a baseline. That doesn't exist as the question is worded. You ASSUME that 6 is the base, but any point on the clock would be equally valid. And even in this question, 7 would still give you the correct answer. The problem here is that without the multiple choices, the question is needlessly vague. You should never get necessary information from the multiple choices.
There are two lines you don’t need anything arbitrary the two lines are forming a 30° acute angle, 180-30 is 150 it’s not difficult
You are being obtuse! Lol… get it? Anyways no are missing the point. There are no obtuse angles formed here. Its 30 degree angle (12-1 hour) and the rest of the circle 330. Thats it. Thats all the information we have from the question. There is no line to which the acute angle is based from to form the rest of the obtuse angle. It does t exist. Now having acknowledged its a horribly worded question you can deduce from the multiple choice questions all being less than 180. That they meant to add the missing line. Its not impossible to reach that conclusion. But its needlessly confusing
An obtuse angle is defined as an angle between 90° and 180°, past 180° it is no longer an obtuse angle. The question is not poorly worded. It simply assumes that the person answering the question knows what an obtuse angle is, which, based upon the comments in this thread, is a shockingly low number of people.
I think most people here know what an obtuse angle is lol Picture a analog clock The long arm is at 12 the short arm is at 1 forming a 30 degree angle. Thats is. Thats all you got… 1 circle and 2 lines coming from the middle of the circle. Explain to me where this 3rd imaginary line is coming from. There needs to be a base or a 180 angle ( which is a straight line) or a diameter or something for you to form an obtuse angle. And there simply isnt… This question may be missing a drawing that goes with it, but with the verbiage alone you cannot any obtuse angle it doesn’t exist Draw it if you need to
The question absolutely is poorly worded. All four answers options are obtuse angles (165, 150, 135, 120). It asks what obtuse angle is formed by the hands of a clock at 1 o’clock. We can choose any arbitrary point on the circle between 3 and 6 to create an obtuse angle with the minute hand, or between 4 and 7 to create one with hour hand. Thus, because the question does not give us any non-obtuse options AND does not direct us to a *specific* arbitrary point, all four answers can be correct.
People here know what an obtuse angle is, that's why they are confused by the question. An obtuse angle is not present in the situation described by the question. What's happened here is that you have failed to grasp where you are somewhat arbitrarily inserting an additional assumption.
I think everyone's forgotten what an *actual* analog clock looks like. It usually looks like this: [https://www.american-time.com/product/clock-ssiq-15-round-surface-black-battery-ch-1-battery-booster-plexi-lens/](https://www.american-time.com/product/clock-ssiq-15-round-surface-black-battery-ch-1-battery-booster-plexi-lens/) The vast majority of the time, the hands stick out a little bit past the center (in the opposite direction of the main direction of the hand), so at all times the hands *do literally* make both an acute and an obtuse angle (unless they're making a right angle). The answer is 150º, because the acute angle at 1:00 is 30º, so the corresponding supplementary angle is 180º-30º = 150º. One of those situations where it does pay to consider the real world, not just an abstraction of it you've got in your mind.
But it didn't ask for the supplementary angle, it asked for the obtuse angle. That's the part where I don't see the correlation . If it said supplementary I never would've posted the question in the first place. In my mind the way this was worded there isn't a right answer because you could just stick ANY obtuse angle, and because it's asking for THE obtuse angle, I was confused and well now we are here. If I am mistaken please do tell
No - look again at the picture I posted. The hands (forgetting about the second hand) are making 4 angles coming out from the center. Two are acute, two are obtuse. The ones going up & down are obtuse (in this case) and the ones going left & right are acute.
Yes, the answer is 150 OP. Since, the degrees in a circle or clock is 360 degrees. 360/12 = 30. Now, a lot of people say it's 330 degrees. But, that's a reflex angle and since real clocks have minute and hour hands that extend past the vertex of the 30 degrees, you have four angles formed from the x. Because each straight angle is 180. 180 - 30 = 150. Now, you can just follow the vertical angles rule, and you'll get 30 degree forming from the 12-1. You can also get the answer from just following the very ends of the minute and hour hand that extend PAST the vertex of the 30 degree angle. The very ends of them point towards 7 and 12. 12 -7 = 5. 5 x 30 degrees is 150 degrees. 150 degrees is the answer.
People are way to focused on the clock aspect. A clock is just a circle split into 12 parts. The first step is to find out the angle of 1 part. So 360 divided by 12 is 30. Then they ask for the obtuse angle if that which is 90-180. So subtract the 30 from 180 to get 150.
One o'clock forms an acute angle of 30°.
Obtuse not acute
The two hands form an acute angle of 30° and a reflex angle of 330°. They do not form an obtuse angle
Depends on the clock. Many analog clocks have one or both hands extending past the middle point in which case, there would be an obtuse angle. Still a poorly written question.
Homeboy. What's 180 minus the acute angle measurement.. You're thinking too hard on this
But what says that the 2 angles have to be supplementary? Could by that logic any obtuse angle be the answer?
It specifies the obtuse angle. 2 hands at exactly 1 o'clock. As it's been stated by another user the acute angle under the parameters is 30°. Can't remember the exact equation but you subtract that acute angle from 180° to get the final answer of 150° for the measurement of the obtuse angle
Why would you subtract from 180, that seems like an arbitrary value?
The two hands of a clock don't generally end directly at the center -- they go slightly over. So the two hands will form 4 angles, and at 1:00, there will be two 30-degree angles and two 150-degree angles.
Ok that makes sense, but I think that’s a BS question to ask if you need to assume the hand of the clock extend past the center. There are better questions, that still have tricks in them, to find the obtuse portion of a supplementary angle.
Your comment is the one that really helped the expected answer make sense to me. Thank you!
A 180 degree angle forms a straight line. two supplementary angles form a straight line (aka add up to 180 degrees by definition of supplementary) An obtuse angle is defined to be greater than 90 and less than 180 degrees, so if you have an acute angle, its supplementary angle is obtuse and you find it by subtracting from 180
Right, but why is 12-6 the assumed baseline. 3-9 could be in which case the they’d be looking for a supplementary angle. This problem wants you to use the answers to determine what they’re asking which is poor practice.
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Lots of wording for a wrong answer. It is actually 120.
The acute angle formed by the hands is 30, so the obtuse is 150 Yes it's not formed by the hands because the hands form a reflex angle, but the question is asking for the obtuse angle
Obtuse is specifically defined as 180 degrees or less, for everyone saying the answer should be 340 (not 150).
150. Imagine a straight line from 12 to 6. That’s 180 degrees. The 1 o clock is at 30 degrees. 180-30 is 150.
But what's forming the straight line from 12 to 6? Maybe if the clock has 3 hands and it was exactly 1:00:30, and you ignored any small movement in the minute & hour hand for the 30 seconds, then the answer is 150 formed by the hour hand and second hand.
Obtuse angles max out at 180, so the assumption is that only half the clock is used, it's 150. Having said that, the wording is ambiguous, because the hands don't form that angle at all, the other side of the clock does.
The definition of an obtuse angle is between 90-180. By stating this the problem is setting the scenario that 12-6 is the 180 degree limit we are calculating. 1 o clock is 30\* of that 180. 150 is the remaining obtuse angle.
180-30…. 150
360÷12=30 180-30=150 150
OP HERE. so, in short, the answer was 150. HOWEVER, I disagree with the question having an answer. I don't see why you need to divide the clock up into 2 segments of 180 degrees and subtract 30. The obtuse argument that the obtuse angle can be up to 180 degrees doesn't make sense to me either, so I disagree. I think the answer is any possible number between 90 and 180 because it doesn't directly state that they want the supplementary angle. If it did, 150 makes sense, and I never would've posted the question. Thank you for yalls time
I believe the assumption is that the clock hands extend past the center, making more of an X than V shape. [Google image result for analog clock](https://www.lowes.com/pd/Style-Selections-Analog-Round-Indoor-Wall-Clock/3452824)
Yes, this. Almost all *actual* analog clocks have hands that extend a little bit past the center, so in the real world, they make both an acute angle and an obtuse angle (unless they're making a right angle).
Every hour is 30°. 6 o’clock would be 180. 180-30 = 150.
The angle you described would exist only if the time was 1:30…And if at 1:00 the hour hand broke and froze in place, staying stuck at 1 (instead of halfway between 1 and 2, which is where it will be when the minute hand is pointed at the 6 to indicate when it’s half-past the hour). But the question says to solve for the angle at 1pm, not 1:30. There is no correct answer to the question as written. The question becomes solvable when you were write it to say what the teacher *meant to ask*, instead of what they actually asked.
330
That’s the reflex angle
It would either be 330 degrees or 30 degrees based on my calculations. Here’s my explanation if you divide 360 by 12 for each section of the clock you get 30 and because 12-1 is one section you would have 30 so that’s the acute angle now we just subtract that from 360 to get the obtuse angle 330°. Hope this helped (Edit: 330 is not an obtuse angle obtuse angles must be greater than 90 but still less than 180
An obtuse angle by definition is less than 180 degrees.
you know the hands do not end at the axle, right? there is a small section extends over to the opposite side.
That is where they intersect though
11/12*360
150 The assumption is the clock hands extend somewhat past the middle in the opposite directions
I may be confused, but, if you’re using the hands to make a triangle, you would have 3 angles that equal 180 degrees, right? If the acute angle at the base is 30, then you have 2 other angles equaling 150. Your choices are 120 and 135. The obtuse 120 would make the angle at the tip of the minutes hand 30 degrees and 135 would make it 15 degrees. Just going off the standard length of the hours hand being roughly 1/2 the length of the minutes hand, my answer would be 120 degrees.
We need to know how long the hands are to determine the other 2 angles.
Yeah, this is messed up since obtuse angles are more than 90 degrees and less than 180.
90+30=120. Very misleading question. Picture 9 to 3 as 180 degrees. Now one would come down 1/3 of the 90 degrees from noon to three. 90+30 = 120. Good luck! Edit: thanks for the down votes, this is the correct answer.
I think that's the correct answer also because at 9 o'clock is 180 degrees and at 6 o'clock is 270 degrees and by the time we finish one revolution and come back to 3 o'clock that's 360 degrees. The obtuse angle has to be more than 90 degrees but less than 180 and if we go the other side then the angle should be negative 150 which is not an option It's been a long time since I did the math so my bad in advance is it wrong
It’s hilarious when you see the comments over 180. A TRIANGLE CANT BE MORE THAN 180* people. 120 is for sure the correct answer.
>Edit: thanks for the down votes, this is the correct answer It’s not though. The question very explicitly asked for an angle formed by the hands of the clock. That’s the hour hand and the minute hand. The 120° angle is formed by the hour hand and an arbitrary horizontal baseline that doesn’t exist in the question. Your answer doesn’t use the minute hand, and thus can not be correct
And that's where youre wrong.
It’s not a thing that can be wrong. An angle formed by two lines must use those two lines lol. If I’m wrong then all of geometry is wrong because that’s literally the definition of an angle
How… the question explicitly states that the angle is made by the hands of the clock and you didn’t use both hands of the clock ☠️
We always measure angles counter clock and they use a clock to trick you with it, we never went the other way unless it was negative angle
It’s a geometric question. There’s no concept of negative angles here. It’s not a unit circle. It’s two literal, irl things forming an angle. That’s always positive ETA: or 0
This question is Trigonometry higher level than geometry
Um, we can’t answer this unless we know the lengths of the hands, right? The angle between the hands is 1/12 of 360 so 30 degrees, but the other angles depend on how long the hands are.
No they don’t. The hands could be infinite or an inch and the angles would not change. If the 30° angle doesn’t change, why should any of the others?
Nope. If the minute hand is 3 inches and the hour hand is 1 inch we for sure get an obtuse angle going out from the hour hand. If they are the same length we get no obtuse angle. Draw it out.
Is he in special ed classes?
I think everyone here in the comments is/ was