Question

1. find the m∠1. name the angle pair used.

Explanation:

Step1: Identify angle - pair relationship

For the first set of parallel - lines and transversal, ∠1 and the 42° angle are vertical angles. Vertical angles are equal.

Step2: Determine the measure of ∠1

Since vertical angles are equal, m∠1 = 42°.

For the second set of parallel - lines and transversal, ∠1 and the 62° angle are corresponding angles. Corresponding angles are equal when the lines are parallel. So m∠1 = 62°.

For the third set of parallel - lines and transversal, ∠1 and the 134° angle are alternate exterior angles. Alternate exterior angles are equal when the lines are parallel. So m∠1 = 134°.

Answer:

First case: m∠1 = 42°, angle - pair: vertical angles
Second case: m∠1 = 62°, angle - pair: corresponding angles
Third case: m∠1 = 134°, angle - pair: alternate exterior angles