Question

find the measure of the missing angles. answer attempt 2 out of 2 d = 108° e = 72° f = 108°

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. Angle $e$ and the given $72^{\circ}$ angle are vertical angles, so $e = 72^{\circ}$.

Step2: Use linear - pair property

A linear pair of angles sums to $180^{\circ}$. Since $e = 72^{\circ}$, and $e$ and $f$ form a linear pair, then $f=180 - 72=108^{\circ}$.

Step3: Use linear - pair property for $d$

The right - angle mark indicates a $90^{\circ}$ angle adjacent to $d$. The sum of angles around a point on a straight line is $180^{\circ}$. If we assume the right - angle and $d$ are part of a linear pair, and since the other non - right angle related to the vertical - angle relationships is $72^{\circ}$, then $d = 180-(72)=108^{\circ}$.

Answer:

$d = 108^{\circ}$, $e = 72^{\circ}$, $f = 108^{\circ}$