Suppose triangle $UVW$ has vertices $U=(1,1)$, $V=(1,4)$, and $W=(4,1)$ in the $xy$-plane. Triangle $XYZ$ has vertices $X=(1,1)$, $Y=(1,4+s)$, and $Z=(4+s,1)$, where $s>0$. If the measure of $\angle V$ is $z^{\circ }$, what is the measure of $\angle Z$?