Question

find the measure of the missing angles.

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. Angle $x$ and the $41^{\circ}$ angle are vertical angles. So $x = 41^{\circ}$.

Step2: Use complementary - angle property

The right - angle and angle $y$ and the $41^{\circ}$ angle are on a straight line. Since the sum of angles on a straight line is $180^{\circ}$ and one of the angles is a right - angle ($90^{\circ}$), we have $y+90^{\circ}+41^{\circ}=180^{\circ}$. Then $y=180^{\circ}-90^{\circ}-41^{\circ}=49^{\circ}$.

Answer:

$x = 41^{\circ}$, $y = 49^{\circ}$