Question

find $m\angle vyw$.
$m\angle vyw = \square^{\circ}$
image of angle diagram with $\angle tyw$ as right angle, $\angle tyv = 31^\circ$, and $\angle vyw$ unknown, plus a calculator interface

Explanation:

Step1: Identify right angle

$\angle TYW = 90^\circ$ (since $WY \perp TX$)

Step2: Calculate target angle

$m\angle VYW = \angle TYW - \angle TYP$
$m\angle VYW = 90^\circ - 31^\circ$

Answer:

$59^\circ$