Triangles $PQR$ and $XYZ$ are congruent. The measure of angle $P$ is $40^{\circ }$, and the measure of angle $Q$ is $80^{\circ }$. If vertex $P$ corresponds to vertex $X$, vertex $Q$ corresponds to vertex $Y$, and vertex $R$ corresponds to vertex $Z$, what is the measure of angle $Z$?