Finding the angles and area of unusual shapes 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.

My attempt:


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*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.

2) Note $ \angle ABD = 90 -25 =65$, which yields $x=65 -25 =40$ due to isosceles triangle.
3) The shaded area is equal to the area of the quadrilateral minus the areas of the two small right triangles. Thus,
$$A= \frac 12\cdot 4(x+4) + \frac12 \cdot 6(2+y) -\frac12 \cdot 4x -\frac12\cdot 6y=14$$
where $x$ and $y$ are the unknown segment lengths that cancel out in the difference.
