Question

find the measure of the missing angles.

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. Angle $x$ and the $64^{\circ}$ angle are vertical angles. So $x = 64^{\circ}$.

Step2: Use linear - pair property

The sum of angles in a linear pair is $180^{\circ}$. Angle $y$ and the $64^{\circ}$ angle form a linear pair. So $y=180 - 64$.
$y = 116^{\circ}$

Answer:

$x = 64^{\circ}$, $y = 116^{\circ}$