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 angle \(d\)

From the figure, we can see that angle \(d\) is a right - angle. By the definition of a right - angle, \(d = 90^{\circ}\).

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

We know that the sum of angles on a straight line is \(180^{\circ}\). The angle of \(78^{\circ}\) and angle \(f\) form a straight line. So, \(78^{\circ}+f = 180^{\circ}\). Then \(f=180^{\circ}-78^{\circ}=102^{\circ}\).

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

Angle \(e\) and the angle of \(78^{\circ}\) are vertical angles. By the vertical - angles theorem (vertical angles are equal), \(e = 78^{\circ}\).

Answer:

\(d = 90^{\circ}\), \(e = 78^{\circ}\), \(f = 102^{\circ}\)