In the figure below, WPRT is a square. QWU and SWV are straight lines. $\angle QWP = 13^\circ$ and $\angle SWT = 28^\circ$. Find $\angle UWV$.

1. Find the angle $\angle SWQ$ inside the square.

Since $WPRT$ is a square, the interior angle at $W$ is $90^\circ$, so $\angle TWP = 90^\circ$.
$\angle SWQ = 90^\circ - \angle SWT - \angle QWP$
$\angle SWQ = 90^\circ - 28^\circ - 13^\circ = 49^\circ$

2. Use vertically opposite angles to find $\angle UWV$.

Since $QWU$ and $SWV$ are straight lines intersecting at $W$, $\angle UWV$ and $\angle SWQ$ are vertically opposite angles.
$\angle UWV = \angle SWQ = 49^\circ$