In the figure below, VWXY is a kite. WYZ is a straight line. $\angle VWY = 36^\circ$ and $\angle WVY = \angle WXY = 90^\circ$. Find $\angle VYX$.

1. Find angle VYW in triangle VWY

In $\triangle VWY$, the sum of angles is $180^\circ$.
$\angle VYW = 180^\circ - \angle WVY - \angle VWY$
$\angle VYW = 180^\circ - 90^\circ - 36^\circ = 54^\circ$

2. Use the symmetry of the kite to find angle XYW

A kite is symmetrical about its main diagonal WY.
Therefore, $\triangle VWY$ is congruent to $\triangle XWY$, so $\angle XYW = \angle VYW = 54^\circ$.

3. Calculate the total angle VYX

$\angle VYX = \angle VYW + \angle XYW$
$\angle VYX = 54^\circ + 54^\circ = 108^\circ$