Question

two parallel lines are cut by a transversal as shown below.
suppose ( m angle 7 = 48 ^ { circ } ). find ( m angle 2 ) and ( m angle 4 ).

Explanation:

Step1: Find \(m\angle2\)

Since \(\angle2\) and \(\angle7\) are alternate exterior angles. When two parallel lines are cut by a transversal, alternate exterior angles are congruent. So \(m\angle2 = m\angle7\). Given \(m\angle7 = 48^{\circ}\), then \(m\angle2=48^{\circ}\).

Step2: Find \(m\angle4\)

\(\angle4\) and \(\angle2\) are supplementary angles (they form a linear - pair). The sum of the measures of angles in a linear - pair is \(180^{\circ}\). So \(m\angle4=180^{\circ}-m\angle2\). Substitute \(m\angle2 = 48^{\circ}\) into the formula: \(m\angle4=180 - 48=132^{\circ}\).

Answer:

\(m\angle2 = 48^{\circ}\)
\(m\angle4 = 132^{\circ}\)