Question

an angle measures 76° less than the measure of its complementary angle. what is the measure of each angle? and

Explanation:

Step1: Define the angles

Let one angle be $x$. Its complementary angle is $90 - x$.

Step2: Set up the equation

Given that one angle measures 76° less than its complementary angle, so $x=(90 - x)-76$.

Step3: Solve the equation

First, expand the right - hand side: $x = 90 - x-76$. Then simplify to get $x = 14 - x$. Add $x$ to both sides: $x+x=14$, which gives $2x = 14$. Divide both sides by 2: $x = 7$.

Step4: Find the complementary angle

The complementary angle is $90 - x=90 - 7 = 83$.

Answer:

7 and 83