Question

two parallel lines are intersected by a third line so that angles 1 and 5 are congruent.
which statement is true about angles 3 and 5?
○ they are acute.
○ they are congruent.
○ they are complementary.
○ they are supplementary.

Explanation:

First, we use the given that angles 1 and 5 are congruent, which confirms the two horizontal lines are parallel (corresponding angles congruent implies parallel lines). Angles 3 and 5 are consecutive interior angles (also called same-side interior angles) formed by a transversal cutting parallel lines. By the consecutive interior angles theorem, these angles add up to 180 degrees, meaning they are supplementary. We cannot confirm they are acute (they could be obtuse/acute pairs), they are not congruent (unless they are both 90 degrees, which is not stated), and they are not complementary (sum to 90 degrees, which is not the case here).

Answer:

They are supplementary.