Question

find the measure of the missing angles. find the measure of the missing angles. answer d = e = f =

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. Angle $d$ and the angle with measure $69^{\circ}$ are vertical angles, so $d = 69^{\circ}$.

Step2: Use linear - pair property

A linear - pair of angles sums to $180^{\circ}$. The angle with measure $32^{\circ}$ and the angle composed of $e$ and $69^{\circ}$ form a linear pair. Let's first find the measure of the angle adjacent to the $32^{\circ}$ angle. It is $180 - 32=148^{\circ}$. Then, since this angle is the sum of $e$ and $69^{\circ}$, we have $e=148 - 69 = 79^{\circ}$.

Step3: Use vertical - angle property again

Angle $f$ and the angle with measure $32^{\circ}$ are vertical angles, so $f = 32^{\circ}$.

Answer:

$d = 69^{\circ}$, $e = 79^{\circ}$, $f = 32^{\circ}$