Question

two parallel lines are cut by a transversal as shown below. suppose m∠3 = 37°. find m∠5 and m∠8.

Explanation:

Step1: Identify angle - relationship for ∠5

∠3 and ∠5 are alternate - interior angles. When two parallel lines are cut by a transversal, alternate - interior angles are congruent. So \(m\angle5=m\angle3\).
Since \(m\angle3 = 37^{\circ}\), then \(m\angle5=37^{\circ}\).

Step2: Identify angle - relationship for ∠8

∠3 and ∠8 are corresponding angles. When two parallel lines are cut by a transversal, corresponding angles are congruent. So \(m\angle8=m\angle3\).
Since \(m\angle3 = 37^{\circ}\), then \(m\angle8 = 37^{\circ}\).

Answer:

\(m\angle5 = 37^{\circ}\), \(m\angle8=37^{\circ}\)