x + y + z + w = 360 because... Uh. I don't remember what the terms to use are but it does. It's a full circle. It's 4 points and 4 angles.

2 (x + y) = 360 because substitute x + y = z + w

x + y = 180 because you divide each side by 2

because x + y is 180, AOB is a line.

That's the best I can do. I may have forgotten a few steps about things you can't assume.