My friend sent me the following geometry problems. I think I have the first one, but I think the 2nd and 3rd are unsolvable, although I could be missing something.
I'm pretty sure this one is 1080. I'm having a hard time writing out my explanation here, but I can justify it on paper. The idea is that the outer shape (if we ignore the triangles) is an octagon, and the sum of its angles is 1080, and I can show that the sum of the marked angles is also 1080.
I don't think this one gives us enough information. If we moved the point D left or right, the angle of $x$ would change and the constraints would still be satisfied.
I can't figure out the answer to this one. I think it's unsolvable as well, but I can't prove it like #2. We can't find the area of anything in this picture. The shaded region and the whole shape are both close to being a trapezoid, but they aren't.