Question

if a || b and m∠1 = 138, what is m∠5?

Explanation:

Step1: Find the measure of ∠3

Since ∠1 and ∠3 are supplementary angles (they form a linear pair), we know that \(m\angle1 + m\angle3=180^{\circ}\). Given \(m\angle1 = 138^{\circ}\), then \(m\angle3=180^{\circ}- 138^{\circ}=42^{\circ}\).

Step2: Use the property of parallel lines

Because \(a\parallel b\), ∠3 and ∠5 are alternate - interior angles. Alternate - interior angles are congruent when two parallel lines are cut by a transversal. So \(m\angle5 = m\angle3\).

Answer:

\(42^{\circ}\)