Question

find the measure of the missing angles.

Explanation:

Step1: Use vertical - angle property

Vertical angles are equal. Angle \(e\) and the \(51^{\circ}\) angle are vertical angles, so \(e = 51^{\circ}\).

Step2: Use linear - pair property

The sum of angles in a linear pair is \(180^{\circ}\). Since \(e\) and \(f\) form a linear pair, \(e + f=180^{\circ}\). Substituting \(e = 51^{\circ}\), we get \(f=180 - 51=129^{\circ}\).

Step3: Use right - angle property

Given that the lower part shows a right - angle, \(d = 90^{\circ}\).

Answer:

\(d = 90^{\circ}\), \(e = 51^{\circ}\), \(f = 129^{\circ}\)