Question

an angle measures 80° less than the measure of its complementary angle. what is the measure of each angle? \boxed{\space}° and \boxed{\space}°

Explanation:

Step1: Define variables

Let the measure of the angle be $x$ degrees. Then its complementary angle is $(90 - x)$ degrees.

Step2: Set up equation

The angle measures 80° less than its complementary angle, so $x=(90 - x)-80$.

Step3: Solve the equation

Simplify the equation: $x = 90 - x - 80$ → $x = 10 - x$ → $x+x = 10$ → $2x = 10$ → $x = 5$.

Step4: Find complementary angle

The complementary angle is $90 - 5 = 85$ degrees.

Answer:

5° and 85°