Question

Repost: I don't want anyone to give me the answer. I just need to know the best way to solve it.

Answer 1

This is simple :p 
The answers are all already there for you.
Here, think about it as two triangles instead of a parallelogram. The triangles are BOTH EXACTLY identical, so what one triangle has, the other will have!
We all know triangles should ALWAYS equal up to 180 degrees.
Angle Z is identical to another point.
The unmarked angle with no letter is identical to another point, right next to it. Use that into, and you can find out angles x and y, as all triangles equal to 180 degrees