Question

6 if ( p parallel q ) and ( m angle 3 = 132 ^ { circ } ), find ( m angle 5 ).

Explanation:

Step1: Find the measure of \(\angle4\)

Since \(\angle3\) and \(\angle4\) are supplementary angles (they form a linear pair), \(m\angle3 + m\angle4=180^{\circ}\). Given \(m\angle3 = 132^{\circ}\), then \(m\angle4=180^{\circ}- 132^{\circ}=48^{\circ}\).

Step2: Use the property of alternate - interior angles

Because \(p\parallel q\), \(\angle4\) and \(\angle5\) are alternate - interior angles. Alternate - interior angles are congruent when two parallel lines are cut by a transversal. So \(m\angle5=m\angle4\).

Answer:

\(48^{\circ}\)