Question

find ( mangle vyw ).
( mangle vyw=square^{circ} )

Explanation:

Step1: Analyze the angle relationship

We know that \( \angle TYX = 180^{\circ}\) (a straight - line angle). Given \( \angle WYX=90^{\circ}\) (right - angle) and \( \angle VYT = 31^{\circ}\).
The sum of \( \angle VYT\), \( \angle VYW\) and \( \angle WYX\) is \( 180^{\circ}\). So, we can use the formula \(m\angle VYT+m\angle VYW + m\angle WYX=180^{\circ}\).

Step2: Solve for \(m\angle VYW\)

Substitute the known values into the formula: \(31^{\circ}+m\angle VYW+90^{\circ}=180^{\circ}\).
First, simplify the left - hand side: \(m\angle VYW+(31^{\circ} + 90^{\circ})=m\angle VYW + 121^{\circ}\).
Then, solve for \(m\angle VYW\) using the equation \(m\angle VYW+121^{\circ}=180^{\circ}\).
Subtract \(121^{\circ}\) from both sides: \(m\angle VYW=180^{\circ}-121^{\circ}\).

Answer:

\(59\)