Question

1. ∠a and ∠b are complementary. ∠a is twice as big as ∠b. how big is each angle? m∠a =__ m∠b=__

Explanation:

Step1: Set up equations

Let \(m\angle B = x\). Since \(\angle A\) is twice as big as \(\angle B\), then \(m\angle A=2x\). And because \(\angle A\) and \(\angle B\) are complementary, \(m\angle A + m\angle B=90^{\circ}\), so \(2x + x=90^{\circ}\).

Step2: Solve for \(x\)

Combine like - terms: \(3x = 90^{\circ}\). Then \(x=\frac{90^{\circ}}{3}=30^{\circ}\).

Step3: Find \(m\angle A\)

Since \(m\angle A = 2x\), substituting \(x = 30^{\circ}\), we get \(m\angle A=2\times30^{\circ}=60^{\circ}\).

Answer:

\(m\angle A = 60^{\circ}\), \(m\angle B=30^{\circ}\)