Question

an angle is equal to one - fifth its complement. find the angles measure.

Explanation:

Step1: Define the angle and its complement

Let the angle be $x$. Its complement is $90 - x$.

Step2: Set up the equation

Given $x=\frac{1}{5}(90 - x)$.

Step3: Solve the equation

Multiply both sides by 5: $5x=90 - x$.
Add $x$ to both sides: $5x+x = 90$, so $6x=90$.
Divide both sides by 6: $x = 15$.

Answer:

$15^{\circ}$