#### Answer

$m \angle R = 145^{\circ}$

#### Work Step by Step

In congruent polygons, vertices are named in the exact order of their matching vertices.
If $WXYZ$ is congruent to $PQRS$, then vertex $W$ corresponds to vertex $P$, vertex $X$ corresponds to vertex $Q$, vertex $Y$ corresponds to vertex $R$, and vertex $Z$ corresponds to vertex $S$.
Therefore, $\angle R$ is congruent to $\angle Y$. So, $m \angle R$ is equal to $m \angle Y$. If $m \angle Y$ is $145^{\circ}$, then $m \angle R$ is $145^{\circ}$.