Question

find the measure of the missing angles.

Explanation:

Step1: Find angle x

Since the right - angle is 90°, and one part of it is 30°. We use the fact that the sum of angles in a right - angle is 90°. So $x + 30^{\circ}=90^{\circ}$, then $x=90^{\circ}- 30^{\circ}$.
$x = 60^{\circ}$

Step2: Find angle y

The sum of angles on a straight - line is 180°. The right - angle is 90° and angle x is 60°. So $y+90^{\circ}+x = 180^{\circ}$. Substitute $x = 60^{\circ}$ into the equation: $y+90^{\circ}+60^{\circ}=180^{\circ}$, then $y=180^{\circ}-(90^{\circ}+60^{\circ})$.
$y = 30^{\circ}$

Answer:

$x = 60^{\circ},y = 30^{\circ}$