Question

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

Step2: Substitute and solve

Substitute $x = 5y$ into $x + y=90^{\circ}$. We get $5y+y=90^{\circ}$, which simplifies to $6y = 90^{\circ}$. Then $y=\frac{90^{\circ}}{6}=15^{\circ}$.

Step3: Find the other angle

Since $x = 5y$, then $x=5\times15^{\circ}=75^{\circ}$.

Answer:

$75$ and $15$