Question

which equation shows that ∠x is complementary to a 15° angle? a ∠x - 15° = 90° b ∠x + 15° = 180° c ∠x + 15° = 90°

Explanation:

Step1: Recall complementary angles

Complementary angles sum to \(90^\circ\). So, if \(\angle X\) is complementary to \(15^\circ\), their sum should be \(90^\circ\).

Step2: Analyze each option

• Option A: \(\angle X - 15^\circ = 90^\circ\) implies \(\angle X = 105^\circ\), not complementary.
• Option B: \(\angle X + 15^\circ = 180^\circ\) implies supplementary (sum to \(180^\circ\)), not complementary.
• Option C: \(\angle X + 15^\circ = 90^\circ\) fits the definition of complementary angles.

Answer:

C. \(\angle X + 15^\circ = 90^\circ\)