Question

1. ∠1 and ∠2 are supplementary angles. ∠1 and ∠3 are vertical angles. if the m∠2 = 23°, find m∠3.

Explanation:

Step1: Recall supplementary - angle property

Supplementary angles add up to 180°. Since ∠1 and ∠2 are supplementary, \(m\angle1 + m\angle2=180^{\circ}\). Given \(m\angle2 = 23^{\circ}\), we can find \(m\angle1\) as \(m\angle1=180^{\circ}-m\angle2\).
\[m\angle1 = 180^{\circ}- 23^{\circ}=157^{\circ}\]

Step2: Recall vertical - angle property

Vertical angles are equal. Since ∠1 and ∠3 are vertical angles, \(m\angle1=m\angle3\).
Since \(m\angle1 = 157^{\circ}\), then \(m\angle3 = 157^{\circ}\)

Answer:

\(157^{\circ}\)