Question

find $m\angle vyw$.
$m\angle vyw = \boxed{?}^\circ$

Explanation:

Step1: Identify right angle

$\angle WYX$ is a right angle, so $m\angle WYX = 90^\circ$.

Step2: Use angle sum for linear pair (right angle)

We know $m\angle TYW = m\angle T YV + m\angle VYW$. Since $m\angle TYW = 90^\circ$ and $m\angle TYV = 31^\circ$, we solve for $m\angle VYW$:
$m\angle VYW = 90^\circ - 31^\circ = 59^\circ$.

Answer:

$59$