Question

1. ∠r and ∠s are complementary angles. if ( mangle r = (12x - 3)^circ ) and ( mangle s = (7x - 2)^circ ), find ( mangle r ).

Explanation:

Step1: Recall complementary angles sum

Complementary angles sum to \(90^\circ\), so \(m\angle R + m\angle S = 90^\circ\).
Substitute \(m\angle R=(12x - 3)^\circ\) and \(m\angle S=(7x - 2)^\circ\):
\((12x - 3)+(7x - 2)=90\)

Step2: Solve for \(x\)

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

Step3: Find \(m\angle R\)

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

Answer:

\(57^\circ\)