Question

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

° and °

Explanation:

Step1: Define the angles

Let the angle be $x$ and its complementary angle be $y$. We know that $x + y=90^{\circ}$ (by the definition of complementary angles), and $x = 8y$.

Step2: Substitute $x$ in the first - equation

Substitute $x = 8y$ into $x + y=90^{\circ}$. We get $8y+y=90^{\circ}$.

Step3: Solve for $y$

Combine like - terms: $9y = 90^{\circ}$. Then $y=\frac{90^{\circ}}{9}=10^{\circ}$.

Step4: Solve for $x$

Since $x = 8y$, substitute $y = 10^{\circ}$ into this equation. So $x=8\times10^{\circ}=80^{\circ}$.

Answer:

$80$ and $10$