Question

the measure of an angle is four times the measure of its complementary angle. what is the measure of each angle? ° and °

Explanation:

Step1: Define variables

Let the measure of the angle be $x$ and the measure of its complementary angle be $y$. We know that complementary angles add up to 90 degrees, so $x + y=90$. Also given that $x = 4y$.

Step2: Substitute $x$ in the first - equation

Substitute $x = 4y$ into $x + y=90$. We get $4y+y=90$.

Step3: Combine like - terms

Combine the left - hand side: $5y=90$.

Step4: Solve for $y$

Divide both sides by 5: $y=\frac{90}{5}=18$.

Step5: Solve for $x$

Since $x = 4y$, then $x=4\times18 = 72$.

Answer:

72 and 18