Question

the measure of an angle is four times the measure of its complementary angle. what is the measure of each angle?

Explanation:

Step1: Set up the equation

Let the measure of the complementary angle be \(x\). Then the measure of the other angle is \(4x\). Since complementary angles sum to \(90^{\circ}\), we have \(x + 4x=90\).

Step2: Solve the equation

Combine like - terms: \(5x = 90\). Then divide both sides by \(5\): \(x=\frac{90}{5}=18\).

Step3: Find the measure of the other angle

If \(x = 18\), then \(4x=4\times18 = 72\).

Answer:

\(18\) and \(72\)