Question

1. ∠r and ∠s are complementary angles. if the m∠r = 12x − 3 and m∠s = 7x − 2, find m∠r.

Explanation:

Step1: Recall complementary angles sum to 90°

Since \( \angle R \) and \( \angle S \) are complementary, \( m\angle R + m\angle S = 90^\circ \). Substitute the given expressions: \( (12x - 3) + (7x - 2) = 90 \).

Step2: Simplify and solve for \( x \)

Combine like terms: \( 12x + 7x - 3 - 2 = 90 \) → \( 19x - 5 = 90 \). Add 5 to both sides: \( 19x = 95 \). Divide by 19: \( x = 5 \).

Step3: Find \( m\angle R \)

Substitute \( x = 5 \) into \( m\angle R = 12x - 3 \): \( 12(5) - 3 = 60 - 3 = 57 \).

Answer:

\( 57^\circ \)