the answers here assume that the base is a continuous, straight line
given one of the angles on the left triangle is a right angle on the diagram, but 80 if you calculate it, you can’t assume that
This is a standard way to draw geometric proofs, it’s not at all unreasonable to assume straight lines and unrepresentative angles.
normally in a geometric proof, a right angle is a right angle
This was certainly not my experience in high school. An unlabelled angle could never be assumed. Only angles marked with a square could be taken as right angles.
guess you’re right!
The answer is 125 degrees but the triangle on the left has 190 degrees in it
Nah, the angle isn’t specified as a right angle. We can’t assume it’s 90° just because it’s drawn that way, because it isn’t drawn to scale.
Left triangle has 180° total. 60+40=100, which means that middle line is actually 80°, not 90. And since the opposite side is the inverse, we know it is 100° on the other side.
100+35=135. We know the right triangle also has 180° total, so to find the top corner we do 180-135=45. So that top corner of the right triangle is 45°, meaning x must be 135° on the opposite side.
I mean, it’s visibly an acute angle wether it’s labelled as such or not.
The angle formerly known as twitter
40 + 60 + 35 Godamn It’s kids math.
Either this is drawn wrong or they broke geometry
The triangles aren’t drawn to scale. The middle line isn’t a 90° angle, because it isn’t specifically marked with a square angle in the corner. Triangles always add up to 180°, so the angle in the left triangle is actually 80°, not 90°.
All these people saying its 135 are making big assumptions that I think is incorrect. There’s one triangle (the left one) that has the angles 40, 60, 80. The 80 degrees is calculated based on the other angles. What’s very important is the fact that these triangles appear to have a shared 90 degree corner, but that is not the case based on what we just calculated. This means the image is not to scale and we must not make any visual assumptions. So that means we can’t figure out the angles of the right triangle since we only have information of 1 angle (the other can’t be figured out since we can’t assume its actually aligned at the bottom since the graph is now obviously not to scale).
Someone correct me if I’m wrong.
You’re making the assumption that they are triangles.
135 is correct. Bottom intersection is 80/100, 180-35-100 = 45 for the top of the second triangle. 180 - 45 = 135
Mathematician here; I second this as a valid answer. (It’s what I got as well.)
Random guy who didn’t sleep in middle school here: I also got the same answer.
Random woman who didn’t sleep very well last night. I got a different answer, then thought about it for 10 more seconds and then got 135.
(No I didn’t assume the right angle, my mistake was even dumber. I need a nap.)
You’re making the assumption that the straight line consisting of the bottom edge of both triangles is made of supplementary angles. This is not defined due to the nature of the image not being to scale.
Unless there are lines that are not straight in the image (which would make the calculation of x literally impossible), the third angle of the triangle in the left has to be 80°, making the angle to its right to be 100°, making the angle above it to be 45°, making the angle above it to be 135°. This is basic trigonometry.
You’re overlooking a major assumption on your end. There is nothing in the image that suggests that the bottom of both triangles forms a straight line. The pair of bottom edges are two separate lines. They may or may not form a sum 180° angle. You are assuming the angles are supplementary. We know that the scale of the image is wrong, thus it is not safe to definitively say that the 80° angle’s neighbor is supplementary. They may be supplementary, or the triangles may share a consistently skewed scale, or the triangles may each have separately skewed scales.
This is a basic logical thought process.
What you say makes no sense.
The problem is LITERALLY unsolvable if we can’t assume that all the lines are straight.
The schematic was OF COURSE purposefully drawn in a way to make the viewer assume that the third angle of the left triangle is 90°, making the angle to it’s right also be 90°, but the point of the exercise is to get the student to use ALL the given information instead of presuming right angles.
And NO, assuming all the lines are straight is NOT unreasonable, it is the only way that the problem could ever possibly have a solution.
I’d say that the shape on the left has what appears to be a little kink right near X, so one might infer that the shape on the left might be a quadrilateral. There are blatantly obvious vertices that are not labeled as such, so we can’t assume that the not-quite-straight line is supposed to be straight since other angles are also not explicitly indicated as vertices…
And NO, assuming all the lines are straight is NOT unreasonable, it is the only way that the problem could ever possibly have a solution.
Wow, you got so close to my point but still fell short! My point is that you cannot reach a solution without making assumptions that fundamentally alter the solution. Your math is correct if and only if your straight line assumption is true. It may be a reasonable assumption, but that does not mean it must always be an accurate assumption.
Reasonable assumptions are a fundamental requirement for communication. It’s not that you are wrong in what you are saying. There is a chance that the poser of the question made a visual representation of the triangle’s sides appear to be complementary and appear to construct a straight line across their bases while not actually definitively indicating them as such.
The way these triangle’s are represented is already skewed so perhaps that is what they are trying to do.
The thing is though, at that point they are defying convention and reasonable assumptions so much that they aren’t worth engaging seriously because it’s flawed communication.
The version people are choosing to answer seriously is equivalent to a guy holding up a sign that says “ask me about my wiener to get one in a flash for free!” while standing next to a hot dog stand. If you ask he flashes his junk at you and says cheekily “haha you just assumed wrong! Idiot!”
That’s already dumb enough but some people could see the clues that suggest he was actually intended to flash people the whole time through a series of reasonable assumptions about his outfit lacking pants or the hit dog stand not even being turned on.
Your argument that we can’t assume the line at the bottom is straight is like saying we can’t assume the theoretical trenchcoat man won’t toss a rabid dachshund he was hiding under the coat at us because the hot dog stand has no buns or condiments on it.
You might not be provably wrong but it’s really not worth thinking like an insane person just because a few conventions were defied
There is nothing in the image that suggests that the bottom of both triangles forms a straight line.
Except for the part where it’s a single straight line segment, as depicted in the image. Showing the complimentary angles as an unlabeled approximately right angle is within convention. Showing a pair of line segments that do not form a straight line as a straight line is not.
Exactly.
Add to this that
xis literally impossible to calculate if conventions are not assumed, and absolutely possible to calculate if conventions are followed. Assuming the conventions won’t hold is an irrational position.
I ask you to consider the following picture:
I tell you that the triangles are not to scale. We can definitively say that h = 80° and k = 90°. Note that h + k != 180°. Despite the strange and inconsistent scaling, this meets all requirements of triangles.Now let me take away the defined 50° angle:
Once again, the triangles are not to scale. They are visually the same triangles. You might assume that h + k = 180°, yielding 40° for the missing angle above k. However, if I reveal to you that the missing angle is indeed 50° or 60° or ANY ANGLE (excl. 40°) such that the sum of angles can still be 180°, you and your assumption are suddenly wrong.Perhaps consider nurturing your brain further before making such condescending remarks.
Following your logic, there is no evidence that these are triangles and it is never stated, therefore none of these lines might be straight and the discussion is irrelevant.
which would make the calculation of x literally impossible
Yes.
But that doesn’t mean that line must be straight. It just means if it isn’t, you can’t derive x.
I mean, the assumption shouldn’t be anything about scale. It should be that we’re looking at straight lines. And if we can’t assume that, then what are we even doing.
But, assuming straight lines, given straight lines you find the other side of an intersecting line because of complements.
And if we can’t assume that, then what are we even doing
That’s exactly what the other user is saying. We can’t assume straight lines because the given angles don’t make any sense and thus this graph is literally impossible to make. We’re arguing over literal click bait is what we’re doing.
Why do the labeled angles prevent us from assuming straight lines?
Because the apparently straight lines contradict the labels. As drawn, the unlabeled bottom vertices are clearly 90°, not 80° and 100°. We must either conclude that the labels are incorrect, or that the figure is not drawn to scale. Either way, it’s insoluble.
Because the angles aren’t represented accurately. It could be that the two angles that look like they’re 90° add up to 180°, but they could also not
That’s technically possible, but that’s also an irrational take. The rational take is to assume the problem is solvable given the available information, which means assuming that the lines are straight.
Yes, two angles appear to be 90⁰, but they’re obviously not with the given information. Math conventions nearly always label right angles, so not having the right angle there implies that the angle should not be assumed to be 90⁰. Math conventions in trigonometry also generally assume straight lines unless there’s a visual indicator that they’re not, and those tend to be exaggerated so it’s obvious.
So the rational answer here is that the bottom line is straight and therefore the problem is solvable. Saying otherwise is irrational, because that’s so far away from math conventions.
We can’t assume that the straight line across the bottom is a straight line because the angles in the drawing are not to scale. Who’s to say that the “right angle” of the right side triangle isn’t 144°?
If the scale is not consistent with euclidian planar geometry, one could argue that the scale is consistent within itself, thus the right triangle’s “right angle” might also be 80°, which is not a supplement to the known 80° angle.
I’d argue that the bottom line is indeed one continuous line regardless of how many other lines intersect on it, because there’s nothing indicating that the line is broken at the intersection.
Now the only reason I think the lines are straight at all is use of the angular notations at the ends, which would be horribly misleading to put at the end of curves or broken lines.
Stupid stuff like this is why kids hate math class. Unless the problem says calculate all unmarked angles, those visually 90 degree angles are 90 degrees. It works that way in any non engineering job that uses angles because it’s common sense.
…what? I get that this drawing is very dysfunctional, but are you going to argue that a triangle within a plane can have a sum of angles of 190°?
The sum of the angles of a triangle are always 180°
Yes, I believe I implied this by suggesting that the sum of angles being 190° is absurd.
Nope I’m not saying that. I’m saying this is a gotcha question that demotivates learners.
I see. I agree completely. The only place this belongs is as a thought experiment on making assumptions in geometry.
No, they’re saying that unless you’re already good at this stuff, it’s easy to assume that a visually 90° angle is actually 90° even when it’s not
Your assumption is that it’s a Cartesian coordinate system with 90° angles. But that’s not necessarily the case. You can apply a sheer transformation to correct for the unusual appearance. When you do that, the angles change, but straight lines stay straight and parallels stay parallel. There’s a mathematical term for that, which I can’t remember right now.
This is a standard way to draw geometric proofs, it’s not at all unreasonable to assume straight lines alongside unrepresentative angles. It’s certainly still an assumption, but a conventional one.
That was a good one
I got 55
I think 125
135, that’s not a 90 degree angle in the problem. Just visually.
Oh that’s just a cheap trick. You are right, it’s 80 degrees despite looking like 90 degrees.
Nah, the imagery tricks you. 180 degrees to a line. 180 degrees inside a triangle.
So you can gather the inside unlabeled angle on the triangle on the left is only 80 degrees: (180-[60+40])
So you then know it’s 100 on the right side of that +35 leaves you with 45 degrees left for the top of the right one.
180-45=. 135 degrees
Also if you add up all visible angles you get 135, so I’m sold on that alone. No no no, I won’t hear any rebuttals.
Right one does not depend on the left one. 3rd dimension for the win!
There’s perils in being in 3d
And thinking so much differently.
I like that all the comments are people discussing the diagram.
For the love of dog, you can’t solve this problem without making assumptions that fundamentally change the answer. People are too quick to spot the first error and then make assumptions that are conveniently consistent with the correction.
The only assumption needed to solve the problem is that the bottom line is indeed straight. Generally it will never be assumed in these types of learning practices that a straight line is a lie, because at that point you can never do a single problem ever. However an undefined angle can be cheesed.
Though it still bugs me on a fundamental level they will cheese the angle to bait a person into a wrong answer, it can teach a valuable lesson about verifying information.
We can solve this issue of a straight line being guaranteed by doing this. This actually is probably a really good practice considering the exacting nature of certain disabilities such as ADHD and Autism. However if you live in the US you need to just accept things like this because we will NEVER fund public education properly let alone consider accessibility beyond things mandated by the ADA
Am I stupid or is one triangle unnecessary?
It is necessary. In the left triangle, the angle that is shown to be right is actually 80°, since other angles are 60 and 40, totaling 100.
That just means the drawing us wrong, because that is a right angle there
It’s not wrong. It’s just not right.
that’s on purpose. it checks whether you actually verify information out just make assumptions. you’re not supposed to eyeball things.
135
It pisses me off to no end that what is CLEARLY shown as a 90degree angle is not in fact 90deg, I hate it when they do that.
Also I will sadly admit this can teach people lessons about verifying the information themselves.
GrumbleGrumbleGrumble…
I get you, but it doesn’t clearly indicate the angle in the middle at the base as much as it suggestively waggles its eyebrows towards 90⁰, it could just as easily be 89.9999999999999⁰, although upon zooming in, you can see the line does shift one pixel over on its way up. You simply can’t trust any of the angles as 90⁰ unless it’s got the ∟ symbol (that’s the official unicode) or you’ve measured them yourself, and with that one pixel off-set, it’s decidedly not 90⁰. That’s why you have to do the math.
That’s just what I said but more into the weeds on the detail.
👍
The internal angles of a triangle always add up to 180⁰, therefore the one pixel offset is irrelevant because the unlabelled angle is, despite what the image suggests, 60⁰.
Assuming you’re talking about the triangle on the left, it’s 80⁰:
180 - 60 - 40 = 80. The other two unlabeled angles are 100⁰ and 45⁰ respectively. None of the unlabelled angles are 60⁰.The shape on the left might be a quadrilateral instead of a triangle, with a vertex at the same place as the top vertex of the shape on the right.
It’s enough to say it’s “CLEARLY” not 90⁰.
Another way to look at it is that it is simply a representation of an object. We don’t need to visualize the angles, as the values to the other asks are given. We just need the geometry of the object represented so we can calculate the value of the unlabeled angle. Given that the geometry of the objects is represented as triangles, we can infer that all sides are straight lines, regardless of the type of space the object occupies.
Geometry diagrams in math problems should never be assumed to be to scale
Yes obviously. But it still irritates me as someone who does geometry for a living.
Assuming these are straight lines.
If these aren’t straight lines, drag has no idea what the answer is and thinks it might be impossible to tell.
