Question

find the measure of the missing angles.

Explanation:

Step1: Identify right - angle property

The angle marked as $d$ is a right - angle. By definition, a right - angle measures $90^{\circ}$. So $d = 90^{\circ}$.

Step2: Use vertical - angle property

The angle of $119^{\circ}$ and angle $e$ are vertical angles. Vertical angles are equal. So $e=119^{\circ}$.

Step3: Use supplementary - angle property

The angle of $119^{\circ}$ and angle $f$ are supplementary (they form a straight - line). Since the sum of supplementary angles is $180^{\circ}$, we have $f=180 - 119$. So $f = 61^{\circ}$.

Answer:

$d = 90^{\circ}$, $e = 119^{\circ}$, $f = 61^{\circ}$