Question

which equation shows that ∠a is complementary to a 45° angle? a ∠a - 45° = 90° b ∠a + 45° = 180° c ∠a + 45° = 90°

Explanation:

Step1: Recall Complementary Angles

Complementary angles sum to \(90^\circ\). So, if \(\angle A\) is complementary to \(45^\circ\), their sum should be \(90^\circ\).

Step2: Analyze Each Option

• Option A: \(\angle A - 45^\circ = 90^\circ\) implies \(\angle A = 135^\circ\), not complementary.
• Option B: \(\angle A + 45^\circ = 180^\circ\) implies supplementary (sum to \(180^\circ\)), not complementary.
• Option C: \(\angle A + 45^\circ = 90^\circ\) matches the definition of complementary angles.

Answer:

C. \(\angle A + 45^\circ = 90^\circ\)