geometry question. ._.

SO this question is part of a bigger question. I solved every other
part. But this part doesn't make sense to me. So this is the image

Find the measurements of X, Y , and Z . I think Y is 45. I know x is z-y . So all I need is the measurement of Z.
Thank you in advance.

nvm its 90, 45 and 45

90. It's a thereom

y is 45...inscribed angles are half the arc angles.