Question

two parallel lines are cut by a transversal as shown below. suppose m ∠2 = 76°. find m ∠5 and m ∠7.

Explanation:

Step1: Find \(m\angle5\)

When two parallel lines are cut by a transversal, \(\angle2\) and \(\angle5\) are alternate interior angles. Alternate interior angles are congruent. So \(m\angle5 = m\angle2\).
Since \(m\angle2 = 76^{\circ}\), then \(m\angle5=76^{\circ}\).

Step2: Find \(m\angle7\)

\(\angle2\) and \(\angle3\) are supplementary (\(\angle2+\angle3 = 180^{\circ}\)), but \(\angle3\) and \(\angle7\) are corresponding angles. Corresponding angles are congruent. Also, \(\angle2\) and \(\angle7\) are vertical angles (another approach). Vertical angles are congruent. So \(m\angle7=m\angle2\).
Since \(m\angle2 = 76^{\circ}\), then \(m\angle7 = 76^{\circ}\).

Answer:

\(m\angle5 = 76^{\circ}\)
\(m\angle7=76^{\circ}\)