Question

1. ∠g and ∠h are complementary angles. if m∠g = (6x − 15)° and m∠h = (3x + 6)°, find m∠h.

Explanation:

Step1: Recall complementary angles sum to 90°

Since \( \angle G \) and \( \angle H \) are complementary, \( m\angle G + m\angle H = 90^\circ \). Substitute the given expressions: \( (6x - 15) + (3x + 6) = 90 \).

Step2: Solve for x

Combine like terms: \( 6x + 3x - 15 + 6 = 90 \) → \( 9x - 9 = 90 \). Add 9 to both sides: \( 9x = 99 \). Divide by 9: \( x = 11 \).

Step3: Find \( m\angle H \)

Substitute \( x = 11 \) into \( m\angle H = (3x + 6)^\circ \): \( 3(11) + 6 = 33 + 6 = 39 \).

Answer:

\( 39^\circ \)