Question

1. if ∠a and ∠b are complementary and the measure of ∠a is five times larger than the measure of ∠b, then which of the following is the measure of ∠b? (1) 10° (3) 30° (2) 15° (4) 45°

Explanation:

Step1: Set up equations

Let the measure of $\angle B=x$. Then the measure of $\angle A = 5x$. Since $\angle A$ and $\angle B$ are complementary, $\angle A+\angle B = 90^{\circ}$. So, $5x + x=90^{\circ}$.

Step2: Solve the equation

Combining like - terms, we get $6x=90^{\circ}$. Then, dividing both sides by 6, $x=\frac{90^{\circ}}{6}=15^{\circ}$.

Answer:

(2) $15^{\circ}$