Question

pick the correct statements. ∠1 and ∠5 are complementary angles. ∠1 and ∠3 are vertical angles. ∠1, ∠5, and ∠4 are supplementary angles. ∠2 and ∠3 are supplementary angles. ∠4 and ∠5 are complementary angles.

Explanation:

Step1: Recall angle - relationship definitions

Complementary angles add up to 90 degrees, supplementary angles add up to 180 degrees, and vertical angles are equal.

Step2: Analyze each statement

• For “∠1 and ∠5 are complementary angles”: There is no indication that ∠1+∠5 = 90°, so this is incorrect.
• For “∠1 and ∠3 are vertical angles”: By the definition of vertical angles (opposite angles formed by two intersecting lines), ∠1 and ∠3 are vertical angles, this is correct.
• For “∠1, ∠5, and ∠4 are supplementary angles”: There is no such relationship that ∠1 + ∠5+∠4=180° based on the general properties of intersecting - lines angles, so this is incorrect.
• For “∠2 and ∠3 are supplementary angles”: Since ∠2 and ∠3 form a linear - pair (adjacent angles on a straight line), ∠2 + ∠3=180°, so this is correct.
• For “∠4 and ∠5 are complementary angles”: There is no indication that ∠4 + ∠5 = 90°, so this is incorrect.

Answer:

∠1 and ∠3 are vertical angles; ∠2 and ∠3 are supplementary angles.