Question

m∠1 = by the m∠2 = by the 58° 122° corresponding angles theorem alternate exterior angles theorem consecutive interior angles theorem alternate interior angles theorem vertical angles congruence theorem

Explanation:

Step1: Find \(m\angle1\)

Since \(\angle1\) and the \(122^{\circ}\) angle are consecutive interior angles.
Consecutive interior angles are supplementary. So \(m\angle1 = 180^{\circ}- 122^{\circ}=58^{\circ}\) by the Consecutive Interior Angles Theorem.

Step2: Find \(m\angle2\)

Since \(\angle2\) and the \(122^{\circ}\) angle are vertical angles.
Vertical angles are congruent. So \(m\angle2 = 122^{\circ}\) by the Vertical Angles Congruence Theorem.

Answer:

\(m\angle1 = 58^{\circ}\) by the Consecutive Interior Angles Theorem.
\(m\angle2 = 122^{\circ}\) by the Vertical Angles Congruence Theorem.