Question

find the measure of the missing angles.
answer attempt 1 out of 2
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 sum of angles in a linear - pair is \(180^{\circ}\). For the linear - pair with the \(105^{\circ}\) angle and angle \(e\), we have \(e=180 - 105=75^{\circ}\).

Step3: Use angle - sum property

We know that the sum of angles around a point is \(360^{\circ}\). Also, we can use the fact that \(e + f+32^{\circ}+105^{\circ}=180^{\circ}\) (a straight - line angle). Since \(e = 75^{\circ}\), then \(75^{\circ}+f + 32^{\circ}+105^{\circ}=180^{\circ}\), so \(f=180-(75 + 32+105)=32^{\circ}\).

Answer:

\(d = 105^{\circ}\), \(e = 75^{\circ}\), \(f = 32^{\circ}\)