Question

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

Explanation:

Step1: Use the property of complementary angles

Complementary angles sum to \(90^{\circ}\). So, \((12x - 3)+(7x - 2)=90\).

Step2: Simplify the left - hand side of the equation

Combine like terms: \(12x+7x-3 - 2=90\), which simplifies to \(19x-5 = 90\).

Step3: Solve for \(x\)

Add \(5\) to both sides: \(19x=90 + 5\), so \(19x=95\). Then divide both sides by \(19\): \(x=\frac{95}{19}=5\).

Step4: Find \(m\angle R\)

Substitute \(x = 5\) into the expression for \(m\angle R\): \(m\angle R=(12x-3)^{\circ}=(12\times5 - 3)^{\circ}\).
Calculate \(12\times5-3=60 - 3=57\).

Answer:

\(m\angle R = 57^{\circ}\)