Question

find the measure of the missing angles. answer attempt 4 out of 5 d = ° e = ° f = °

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. Angle $d$ and the $105^{\circ}$ angle are vertical angles, so $d = 105^{\circ}$.

Step2: Use linear - pair property

The $105^{\circ}$ angle and $e$ form a linear pair. A linear pair of angles sums to $180^{\circ}$. So $e=180 - 105=75^{\circ}$.

Step3: Use linear - pair property again

The $32^{\circ}$ angle and $f$ form a linear pair. So $f = 180 - 32=148^{\circ}$.

Answer:

$d = 105^{\circ}$
$e = 75^{\circ}$
$f = 148^{\circ}$