Question

find the measure of the missing angles.

Explanation:

Step1: Find the measure of \(x\)

Vertical angles are equal. \(x\) and \(32^{\circ}\) are vertical angles.
\(x = 32^{\circ}\)

Step2: Find the measure of \(y\)

The sum of angles around a point is \(180^{\circ}\). We know one angle is \(90^{\circ}\) (right - angle) and \(x = 32^{\circ}\).
\(y+90^{\circ}+x=180^{\circ}\)
Substitute \(x = 32^{\circ}\) into the equation:
\(y+90^{\circ}+32^{\circ}=180^{\circ}\)
\(y+122^{\circ}=180^{\circ}\)
\(y=180^{\circ}-122^{\circ}\)
\(y = 58^{\circ}\)

Answer:

\(x = 32^{\circ}\), \(y = 58^{\circ}\)