Question

the measure of an angle is five 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 other angle is \(5x\). Since complementary angles sum to \(90^{\circ}\), we have \(x + 5x=90\).

Step2: Solve the equation

Combine like terms: \(6x = 90\). Divide both sides by \(6\): \(x=\frac{90}{6}=15\).

Step3: Find the other angle

The other angle is \(5x\). Substitute \(x = 15\): \(5\times15 = 75\).

Answer:

\(15\) and \(75\)