Question

which equation shows that a 53° angle is complementary to ∠g ?
a ∠g - 53° = 90°
b ∠g + 53° = 90°
c ∠g + 53° = 180°

Explanation:

Step1: Recall Complementary Angles

Complementary angles sum to \(90^\circ\). So if \(53^\circ\) and \(\angle G\) are complementary, their sum is \(90^\circ\).

Step2: Analyze Each Option

• Option A: \(\angle G - 53^\circ = 90^\circ\) implies \(\angle G = 143^\circ\), not complementary.
• Option B: \(\angle G + 53^\circ = 90^\circ\) fits the complementary angle definition.
• Option C: \(\angle G + 53^\circ = 180^\circ\) is for supplementary angles (sum to \(180^\circ\)), not complementary.

Answer:

B. \(\boldsymbol{\angle G + 53^\circ = 90^\circ}\)