Question

find the measure of the missing angles. answer attempt 2 out of 2 d = 63° e = 96° f = 33°

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. Angle $d$ and the $63^{\circ}$ angle are vertical angles, so $d = 63^{\circ}$. Angle $e$ and the $96^{\circ}$ angle are vertical angles, so $e = 96^{\circ}$.

Step2: Use angle - sum property

The sum of angles around a point is $360^{\circ}$. Also, we can consider a linear - pair or use the fact that in the region where $f$ is located, if we assume the angles are part of a triangle - like formation (using the straight - line property). Since the sum of angles on a straight - line is $180^{\circ}$, and we know two angles in the relevant region are $63^{\circ}$ and $96^{\circ}$, then $f=180-(63 + 96)=33^{\circ}$.

Answer:

$d = 63^{\circ}$, $e = 96^{\circ}$, $f = 33^{\circ}$