Question

which equation shows that a 32° angle is complementary to ∠d ? a ∠d - 32° = 90° b ∠d + 32° = 180° c ∠d + 32° = 90°

Explanation:

Step1: Recall complementary angles

Complementary angles sum to \(90^\circ\). So if \(32^\circ\) and \(\angle D\) are complementary, their sum should be \(90^\circ\).

Step2: Analyze each option

• Option A: \(\angle D - 32^\circ = 90^\circ\) implies \(\angle D = 122^\circ\), not complementary.
• Option B: \(\angle D + 32^\circ = 180^\circ\) implies supplementary (sum to \(180^\circ\)), not complementary.
• Option C: \(\angle D + 32^\circ = 90^\circ\) matches the definition of complementary angles.

Answer:

C. \(\angle D + 32^\circ = 90^\circ\)