Triangles $XYZ$ and $UVW$ are graphed in the $xy$-plane. Triangle $XYZ$ has vertices $X,Y,$ and $Z$ at $(-3,2),(-3,8),$ and $(3,2),$ respectively. Triangle $UVW$ has vertices $U,V,$ and $W$ at $(-3,2),(-3,8+s),$ and $(3+s,2),$ respectively, where $s$ is a positive constant. If the measure of $\angle Y$ is $a^{\circ },$ what is the measure of $\angle W$ ?