Solve the following math problem step by step. The last line of your response should be of the form Answer: \boxed{$Answer} where $Answer is the answer to the problem.

<image>In $\odot Z, \angle W Z X \cong \angle X Z Y, m \angle V Z U=4 x$, $m \angle U Z Y=2 x+24,$ and $\overline{V Y}$ and $\overline{W U}$ are diameters.
Find $m\widehat{U Y}$