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: Set up the equation

Let the measure of the complementary angle be \(x\). Then the measure of the other angle is \(14x\). Since complementary angles sum to \(90^{\circ}\), we have \(x + 14x=90\).

Step2: Solve the equation

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

Step3: Find the measure of the other angle

Substitute \(x = 6\) into \(14x\). So \(14x=14\times6 = 84\).

Answer:

\(6\) and \(84\)