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.
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.
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.
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.
