Question

which angles are complementary to each other? ∠4 and ∠6 ∠3 and ∠1 ∠5 and ∠1 ∠5 and ∠6

Explanation:

Step1: Recall complementary - angle definition

Two angles are complementary if their sum is 90 degrees. Given that ∠3 = 90 degrees, and ∠3+∠4 + ∠5=180 degrees (a straight - line angle), then ∠4+∠5 = 90 degrees. Also, since vertical angles are equal, ∠1 = ∠5 and ∠4 = ∠6.

Step2: Analyze each option

• For ∠4 and ∠6: ∠4 and ∠6 are vertical angles, not complementary.
• For ∠3 and ∠1: ∠3 = 90 degrees, and ∠1+∠3+∠2=180 degrees, so they are not complementary.
• For ∠5 and ∠1: Since ∠1 = ∠5, they are not complementary.
• For ∠5 and ∠6: Since ∠4+∠5 = 90 degrees and ∠4 = ∠6, then ∠5+∠6 = 90 degrees.

Answer:

∠5 and ∠6