Question

this image shows two parallel lines cut by a transversal.
if the measure of angle 8 equals 112 degrees, what is the measure of angle 3?

Explanation:

Step1: Use the property of vertical angles

Vertical angles are equal. So, angle \(8\) and angle \(6\) are vertical angles. Given \(\angle8 = 112^{\circ}\), then \(\angle6=\angle8 = 112^{\circ}\).

Step2: Use the property of consecutive - interior angles

The two parallel lines are cut by a transversal. Consecutive - interior angles are supplementary. \(\angle6\) and \(\angle3\) are consecutive - interior angles. So, \(\angle6+\angle3 = 180^{\circ}\).

Step3: Solve for \(\angle3\)

Substitute \(\angle6 = 112^{\circ}\) into \(\angle6+\angle3 = 180^{\circ}\). Then \(\angle3=180^{\circ}-\angle6\). \(\angle3 = 180 - 112=68^{\circ}\).

Answer:

\(68^{\circ}\)