Question

two parallel lines are cut by a transversal as shown below. suppose ( m angle 7 = 32 ^ { circ } ). find ( m angle 2 ) and ( m angle 4 ).

Explanation:

Step1: Find \(m\angle2\)

When two parallel lines are cut by a transversal, \(\angle2\) and \(\angle7\) are alternate - exterior angles. Alternate - exterior angles are congruent. So \(m\angle2=m\angle7\). Given \(m\angle7 = 32^{\circ}\), then \(m\angle2=32^{\circ}\).

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 \(m\angle2 = 32^{\circ}\) into the formula: \(m\angle4=180 - 32=148^{\circ}\)

Answer:

\(m\angle2 = 32^{\circ}\)
\(m\angle4 = 148^{\circ}\)