Question

question find the measure of the missing angles.

Explanation:

Step1: Identify vertical - angles

Vertical angles are equal. The angle opposite the given $36^{\circ}$ angle is also $36^{\circ}$.

Step2: Identify supplementary angles

The angles adjacent to the $36^{\circ}$ angle are supplementary to it. Let the adjacent angle be $x$. We know that $x + 36^{\circ}=180^{\circ}$. So, $x = 180^{\circ}-36^{\circ}=144^{\circ}$. The angle opposite this $144^{\circ}$ angle (vertical - angle) is also $144^{\circ}$.

Answer:

The missing angles are two angles of measure $36^{\circ}$ and two angles of measure $144^{\circ}$