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 complementary. they are supplementary. they are acute. they are congruent

Explanation:

Step1: Analyze angle relationships

Given two parallel lines cut by a transversal, angle 1 and angle 5 are congruent (corresponding angles, so lines are parallel by converse of corresponding angles postulate). Angle 1 and angle 3 are vertical angles, so \( \angle 1=\angle 3 \). Since \( \angle 1 = \angle 5 \), then \( \angle 3=\angle 5 \) (transitive property). So angles 3 and 5 are congruent.

Step2: Evaluate options

• "They are complementary": Complementary angles sum to \( 90^\circ \), not indicated here.
• "They are supplementary": Supplementary angles sum to \( 180^\circ \), not the case.
• "They are acute": Not necessarily, could be right or obtuse (but since \( \angle 1=\angle 5 \) and if lines are parallel, and angle 3 is equal to angle 1, so angle 3 = angle 5, so congruent).
• "They are congruent": Matches the deduction.

Answer:

They are congruent (the option with "They are congruent" text)