Question

two parallel lines are cut by a transversal as shown below. suppose m∠3 = 46°. find m∠6 and m∠8.

Explanation:

Step1: Find \(m\angle6\)

When two parallel lines are cut by a transversal, \(\angle3\) and \(\angle6\) are alternate interior angles. Alternate interior angles are congruent. So \(m\angle6 = m\angle3\).
Since \(m\angle3 = 46^{\circ}\), then \(m\angle6=46^{\circ}\).

Step2: Find \(m\angle8\)

\(\angle3\) and \(\angle8\) are corresponding angles. Corresponding angles are congruent when two parallel lines are cut by a transversal. So \(m\angle8 = m\angle3\).
Since \(m\angle3 = 46^{\circ}\), then \(m\angle8 = 46^{\circ}\).

Answer:

\(m\angle6 = 46^{\circ}\)
\(m\angle8 = 46^{\circ}\)