Question

the measure of an angle is eight times the measure of its complementary angle. what is the measure of each angle? ° and °

Explanation:

Step1: Set up the equation

Let the measure of the complementary angle be \(x\). Then the measure of the angle is \(8x\). Since complementary angles sum to \(90^{\circ}\), we have \(x + 8x=90\).

Step2: Solve the equation

Combine like terms: \(9x = 90\). Divide both sides by \(9\): \(x=\frac{90}{9}=10\).

Step3: Find the measure of the other angle

If \(x = 10\), then \(8x=8\times10 = 80\).

Answer:

\(10\) and \(80\)