Question

what relationship(s) exist for ∠1 and ∠2? select all that apply
vertical
complementary
supplementary
congruent
linear pair

Explanation:

Step1: Recall angle - relationship definitions

Vertical angles are opposite angles formed by two intersecting lines. Complementary angles add up to 90 degrees. Supplementary angles add up to 180 degrees. Congruent angles have the same measure. A linear - pair is a pair of adjacent angles that form a straight line.

Step2: Analyze the first pair of angles

For the first pair of angles ∠1 and ∠2 formed by two intersecting lines, they are vertical angles. Since vertical angles are congruent, they are also congruent.

Step3: Analyze the second pair of angles

For the second pair of angles ∠1 and ∠2 formed by two intersecting lines, they are vertical angles. Since vertical angles are congruent, they are also congruent.

Answer:

First pair: Vertical, Congruent
Second pair: Vertical, Congruent