Question

find the measure of the missing angles. answer attempt 2 out of 2 d = 46° e = 20° f = 114°

Explanation:

Step1: Use linear - pair property

Since a linear - pair of angles sums to 180°, for the angle with measure 134° and angle \(d\), we have \(d + 134^{\circ}=180^{\circ}\). Solving for \(d\): \(d=180^{\circ}-134^{\circ}=46^{\circ}\).

Step2: Identify vertical angles

Vertical angles are equal. The angle with measure 20° and angle \(e\) are vertical angles, so \(e = 20^{\circ}\).

Step3: Calculate angle \(f\)

The sum of angles around a point is 360°. We know two of the angles are 134° and 20°, and we want to find \(f\). Also, we know \(d = 46^{\circ}\) and \(e = 20^{\circ}\). Considering the angles around the point, we can also use the fact that \(f+20^{\circ}+46^{\circ}=180^{\circ}\) (a straight - line angle). So \(f=180^{\circ}-(20^{\circ}+46^{\circ})=114^{\circ}\).

Answer:

\(d = 46^{\circ},e = 20^{\circ},f = 114^{\circ}\)