In the figure below, VWXY is a rhombus. XYZ is a straight line and $\angle VWY = 36^\circ$. Find $\angle VYZ$.

1. Find $\angle VYW$ using the properties of a rhombus.

In rhombus $VWXY$, all sides are equal, so $VW = VY$. Therefore, $\triangle VWY$ is an isosceles triangle.
$\angle VYW = \angle VWY = 36^\circ$

2. Find the interior angle $\angle VYX$.

The diagonal of a rhombus bisects its interior angles, so $\angle XYW = \angle VYW = 36^\circ$.
$\angle VYX = 36^\circ + 36^\circ = 72^\circ$

3. Find $\angle VYZ$ using angles on a straight line.

Since $XYZ$ is a straight line, $\angle VYZ$ and $\angle VYX$ are supplementary.
$\angle VYZ = 180^\circ - 72^\circ = 108^\circ$