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.

The sum of the angles of a triangle are always 180°

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.