Question

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

Explanation:

Step1: Define the variables

Let the measure of the angle be $x$ degrees and its complementary angle be $y$ degrees. We know that $x + y=90$ (since complementary angles sum to 90 degrees) and $x = 4y$.

Step2: Substitute $x$ in the first - equation

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

Step3: Simplify the equation

Combine like - terms: $5y=90$.

Step4: Solve for $y$

Divide both sides of the equation $5y = 90$ by 5. So, $y=\frac{90}{5}=18$.

Step5: Solve for $x$

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

Answer:

72, 18