Question

finding angle measures given two parallel lines cut by a transversal
two parallel lines are cut by a transversal as shown below.
suppose ( m angle 8 = 79 ^ { circ } ). find ( m angle 2 ) and ( m angle 3 ).

Explanation:

Step1: Find \(m\angle2\)

Since \(\angle2\) and \(\angle6\) are corresponding angles (parallel lines cut by a transversal), and \(\angle6\) and \(\angle8\) are vertical angles (\(\angle6=\angle8 = 79^{\circ}\)), so \(m\angle2 = 79^{\circ}\)

Step2: Find \(m\angle3\)

\(\angle2\) and \(\angle3\) are supplementary angles (\(\angle2+\angle3 = 180^{\circ}\)). Given \(m\angle2=79^{\circ}\), then \(m\angle3=180 - 79=101^{\circ}\)

Answer:

\(m\angle2 = 79^{\circ}\), \(m\angle3 = 101^{\circ}\)