Question

question
find the measure of the missing angles.
answer attempt 2 out of 2
$d = square^{circ}$ $e = 129^{circ}$ $f = 51^{circ}$

Explanation:

Step1: Identify vertical - angle relationship

Vertical angles are equal. Angle \(e\) and the given \(129^{\circ}\) angle are vertical angles, so \(e = 129^{\circ}\).

Step2: Use linear - pair relationship

The angle \(e\) and \(f\) form a linear pair. A linear pair of angles sums to \(180^{\circ}\). So \(f=180 - e\). Substituting \(e = 129^{\circ}\), we get \(f = 180-129=51^{\circ}\).

Step3: Identify right - angle

The square symbol at angle \(d\) indicates it is a right - angle. So \(d = 90^{\circ}\).

Answer:

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