Question

line r intersect lines p and q. which statement must be true about ∠1 and ∠2 in order for line p and q to be parallel. a their measures must sum to 127°. b their measures must equal 53°. c their measures must be supplementary. d their measures must be equal.

Explanation:

Step1: Recall parallel - line property

When two lines are parallel and intersected by a transversal, corresponding angles are equal. ∠1 and the 127 - degree angle are vertical angles, so ∠1 = 127°. For lines p and q to be parallel, ∠1 and ∠2 must be corresponding angles.

Step2: Determine the relationship

If lines p and q are parallel, corresponding angles are congruent. So, the measure of ∠1 must be equal to the measure of ∠2.

Answer:

D. Their measures must be equal.