Question

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

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Explanation:

Step1: Let the measure of the complementary angle

Let the measure of the complementary angle be \(x\) degrees. Then the measure of the other angle is \(14x\) degrees.

Step2: Use the property of complementary angles

Since complementary angles sum to \(90^{\circ}\), we have the equation \(x + 14x=90\).
Combining like - terms: \(15x = 90\).

Step3: Solve for \(x\)

Divide both sides of the equation \(15x = 90\) by \(15\): \(x=\frac{90}{15}=6\).

Step4: Find the measure of the other angle

If \(x = 6\), then the other angle \(14x=14\times6 = 84\).

Answer:

\(6\) and \(84\)