Question

two parallel lines are cut by a transversal as shown below. suppose ( m angle 8 = 79^{circ} ). find ( m angle 1 ) and ( m angle 3 ).

Explanation:

Step1: Find \(m\angle3\)

Since \(\angle3\) and \(\angle8\) are corresponding angles (parallel lines cut by a transversal), \(m\angle3 = m\angle8\).
\(m\angle3=79^{\circ}\)

Step2: Find \(m\angle1\)

Since \(\angle1\) and \(\angle3\) are supplementary angles (\(\angle1+\angle3 = 180^{\circ}\)), \(m\angle1=180^{\circ}-m\angle3\).
Substitute \(m\angle3 = 79^{\circ}\), \(m\angle1=180^{\circ}-79^{\circ}=101^{\circ}\)

Answer:

\(m\angle1 = 101^{\circ}\)
\(m\angle3 = 79^{\circ}\)