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.
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.
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 and basic trigonometry.
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.
Add to this that x is 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.
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.
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
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.
Yes.
But that doesn’t mean that line must be straight. It just means if it isn’t, you can’t derive x.
I ask you to consider the following picture:
Now let me take away the defined 50° angle:
Perhaps consider nurturing your brain further before making such condescending remarks.
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 and basic trigonometry.
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.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.
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