Question

find the measure of the missing angles.
answer
attempt 1 out of 3
d = □° e = □° f = □°

Explanation:

Step1: Find the measure of angle \(d\)

Vertical angles are equal. So \(d = 105^{\circ}\)

Step2: Find the measure of angle \(e\)

\(e+105^{\circ}=180^{\circ}-32^{\circ}\) (linear - pair and vertical - angle relationships). First, \(180^{\circ}-32^{\circ}=148^{\circ}\). Then \(e = 148^{\circ}-105^{\circ}\)
\(e=32^{\circ}\)

Step3: Find the measure of angle \(f\)

\(e + f=180^{\circ}-105^{\circ}\) (linear - pair). Since \(e = 32^{\circ}\), then \(f=180^{\circ}-105^{\circ}-32^{\circ}\)
\(f = 43^{\circ}\)

Answer:

\(d = 105^{\circ}\), \(e = 32^{\circ}\), \(f = 43^{\circ}\)