Question

1. which angles are complementary? a. ∠2 and ∠3 b. ∠3 and ∠4 c. ∠4 and ∠5 d. ∠1 and ∠2 e. ∠3 and ∠5

Explanation:

Step1: Recall complementary - angle definition

Two angles are complementary if their sum is 90 degrees.

Step2: Analyze the figure

In the given figure, we can see that ∠1 is a right - angle (marked with a square), and ∠1+∠2 = 180 degrees (a straight - line angle). Since ∠1 = 90 degrees, then ∠2=90 degrees. Also, ∠1 and ∠2 are adjacent angles that form a straight - line, and ∠1 is a right - angle. We know that ∠3 and ∠5 are vertical angles, ∠4 and ∠2 are vertical angles.
We observe that ∠3+∠4 = 90 degrees because the angle formed by the intersection of the lines where ∠3 and ∠4 are located is a right - angle.

Answer:

b. ∠3 and ∠4