Question

the measure of an angle is five 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 angle is $5x$.

Step2: Recall the property of complementary angles.

Complementary angles add up to $90^{\circ}$, so $x + 5x=90^{\circ}$.

Step3: Solve the equation for $x$.

Combining like - terms, we get $6x = 90^{\circ}$. Then $x=\frac{90^{\circ}}{6}=15^{\circ}$.

Step4: Find the measure of the larger angle.

The larger angle is $5x$, so $5\times15^{\circ}=75^{\circ}$.

Answer:

The measure of the complementary angle is $15^{\circ}$ and the measure of the angle is $75^{\circ}$