Question

1. ∠r and ∠s are complementary angles. if m∠r = (6x − 47)° and m∠s = (x + 4)°, find m∠s.

Explanation:

Step1: Recall complementary angles property

Complementary angles sum to \(90^\circ\). So, \(m\angle R + m\angle S = 90^\circ\).

Step2: Substitute angle expressions

Substitute \(m\angle R=(6x - 47)^\circ\) and \(m\angle S=(x + 4)^\circ\) into the equation: \((6x - 47)+(x + 4)=90\).

Step3: Simplify and solve for \(x\)

Combine like terms: \(7x - 43 = 90\). Add 43 to both sides: \(7x=90 + 43=133\). Divide by 7: \(x=\frac{133}{7}=19\).

Step4: Find \(m\angle S\)

Substitute \(x = 19\) into \(m\angle S=(x + 4)^\circ\): \(m\angle S=(19 + 4)^\circ=23^\circ\).

Answer:

\(23^\circ\)