Question

the measure of an angles supplement is 76° less than the measure of the angle. find the measures of the angle and its supplement. measure of the angle = measure of the angles supplement =

Explanation:

Step1: Let the angle be $x$.

The supplement of the angle is $180 - x$.

Step2: Set up the equation.

Given that the measure of an angle’s supplement is $76^{\circ}$ less than the measure of the angle, so $180 - x=x - 76$.

Step3: Solve the equation for $x$.

Add $x$ to both sides: $180=2x - 76$.
Add 76 to both sides: $180 + 76=2x$, so $256 = 2x$.
Divide both sides by 2: $x = 128$.

Step4: Find the supplement.

The supplement is $180 - x=180 - 128 = 52$.

Answer:

measure of the angle = $128$
measure of the angle’s supplement = $52$