Question

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m∠1 = by the

m∠2 = by the

30° 150° corresponding angles theorem alternate exterior angles theorem
consecutive interior angles theorem alternate interior angles theorem

Explanation:

Step1: Find \(m\angle1\)

The \(150^{\circ}\) angle and \(\angle1\) are consecutive interior angles. Since the sum of consecutive interior angles is \(180^{\circ}\), \(m\angle1 = 180^{\circ}- 150^{\circ}=30^{\circ}\) by the Consecutive Interior Angles Theorem.

Step2: Find \(m\angle2\)

\(\angle1\) and \(\angle2\) are vertical angles. Vertical angles are equal. So \(m\angle2 = 30^{\circ}\) by the Vertical Angles Theorem (not in the given options, but since \(\angle1 = 30^{\circ}\) and \(\angle2\) is vertical to \(\angle1\), and also \(\angle2\) and the \(150^{\circ}\) - adjacent angle (supplementary to \(\angle1\)) are alternate exterior angles. But using the relation from \(\angle1\), \(m\angle2=150^{\circ}\) (as \(\angle2\) and the \(150^{\circ}\) - non - adjacent angle are congruent by Alternate Exterior Angles Theorem. Wait, no, correct way:
The \(150^{\circ}\) angle and \(\angle2\) are Alternate Exterior Angles. So \(m\angle2 = 150^{\circ}\) by the Alternate Exterior Angles Theorem.

Answer:

\(m\angle1 = 30^{\circ}\) by the Consecutive Interior Angles Theorem.
\(m\angle2 = 150^{\circ}\) by the Alternate Exterior Angles Theorem.