Question

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

Explanation:

Step1: Define complementary angles

Let the measure of the complementary - angle be $x$. Then the measure of the given angle is $9x$. Since complementary angles add up to $90^{\circ}$, we have the equation $x + 9x=90$.

Step2: Solve the equation

Combining like - terms, we get $10x = 90$. Dividing both sides of the equation by 10, we have $x=\frac{90}{10}=9$.

Step3: Find the measure of the given angle

The measure of the given angle is $9x$. Substituting $x = 9$ into $9x$, we get $9\times9 = 81$.

Answer:

The measure of the angle is $81^{\circ}$ and the measure of its complementary angle is $9^{\circ}$