Question

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

Explanation:

Step1: Let the measure of the complementary angle be $x$.

The measure of the given angle is $14x$.

Step2: Recall the property of complementary angles.

Complementary angles add up to $90^{\circ}$. So, $x + 14x=90$.

Step3: Combine like - terms.

$15x = 90$.

Step4: Solve for $x$.

$x=\frac{90}{15}=6$.

Step5: Find the measure of the given angle.

The given angle is $14x$, so $14\times6 = 84$.

Answer:

The measure of the complementary angle is $6^{\circ}$ and the measure of the other angle is $84^{\circ}$