Question

find the measure of the missing angles.
answer attempt 1 out of 2
$d = square ^ { circ }$
$e = square ^ { circ }$
$f = square ^ { circ }$

Explanation:

Step1: Find the measure of \(d\)

Vertical angles are equal. The angle of \(105^{\circ}\) and the angle composed of \(d\) and \(32^{\circ}\) are vertical angles. So \(d + 32^{\circ}=105^{\circ}\), then \(d=105^{\circ}- 32^{\circ}\).

$$d = 105 - 32=73^{\circ}$$

Step2: Find the measure of \(e\)

\(e\) and \(105^{\circ}\) are supplementary angles (they form a linear - pair). So \(e+105^{\circ}=180^{\circ}\), then \(e = 180^{\circ}-105^{\circ}\).

$$e=75^{\circ}$$

Step3: Find the measure of \(f\)

\(f\) and \(d\) are supplementary angles (they form a linear - pair). So \(f + d=180^{\circ}\), since \(d = 73^{\circ}\), then \(f=180^{\circ}-73^{\circ}\).

$$f = 107^{\circ}$$

Answer:

\(d = 73^{\circ}\), \(e = 75^{\circ}\), \(f = 107^{\circ}\)