Question

complete each step to show that the sum of the measures of ∠1, ∠2, and ∠3 is 180°.
step 1: m∠1 = m∠4 and m∠2 = m∠5 because ? are congruent.

Explanation:

Step1: Identify Angle Relationship

In the diagram, the two lines are parallel (indicated by the arrow marks), and the transversal creates alternate interior angles. So, \( \angle 1 \) and \( \angle 4 \) are alternate interior angles, and \( \angle 2 \) and \( \angle 5 \) are also alternate interior angles.

Step2: Recall Alternate Interior Angles Theorem

By the Alternate Interior Angles Theorem, when two parallel lines are cut by a transversal, alternate interior angles are congruent. So, \( m\angle 1 = m\angle 4 \) and \( m\angle 2 = m\angle 5 \) because alternate interior angles are congruent.

Answer:

alternate interior angles