Question

two parallel lines are cut by a transversal as shown below. suppose m∠2 = 76°. find m∠5 and m∠7. m∠5 = □° 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 \(m\angle5 = m\angle2\). Given \(m\angle2 = 76^{\circ}\), then \(m\angle5=76^{\circ}\).

Step2: Find \(m\angle7\)

\(\angle2\) and \(\angle7\) are corresponding angles. Corresponding angles formed by two parallel lines and a transversal are congruent. So \(m\angle7 = m\angle2\). Since \(m\angle2 = 76^{\circ}\), then \(m\angle7 = 76^{\circ}\).

Answer:

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