Rectangle divided into three triangles with two lines. One angle is given, what are all the others?

Question

Let's suppose I have a rectangle divided into three triangles in the following way. No lengths of either the rectangle or triangles are known, only one angle is known.

I would like to know how to calculate all the other angles. Here is a sample image of the problem:

This looks so simple but I have no idea even where to start. Where is the trick?

Answer 1

Without further information, you cannot determine any of the other angles, other than the right angles (since you are given a rectangle). If we know one other non-right angle, we can compute all the other angles by simply knowing that the angles of a triangle sum to $180^\circ$.

Answer 2

You have to trust the linear dimensions or you don't have enough information. Otherwise the point can move along the bottom of the rectangle, changing the proportions of the rectangle. Once you do, the left hand triangle is $90-45-45$