Question

What is arc YZ

Answer 1

Do you know measure of angle YVZ?

Answer 2

Would it be 90 degrees

Answer 3

Correct.
And these a theorem that states based on your problem that

<YVZ = 1/2( XU + YZ)
You can use this and what you know to solve for YZ

Answer 4

So then it would be 90=1/2 (38+142)?

Answer 5

Yes. Well all you need to find was YZ and it seems like you got it right
YZ= 142