Question

the measure of an angle’s 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 angle’s supplement =

Explanation:

Step1: Define variables

Let the measure of the angle be $x$ degrees. Then the measure of its supplement is $(x - 76)$ degrees. (Since supplementary angles add up to $180^\circ$, and the supplement is $76^\circ$ less than the angle)

Step2: Set up the equation

We know that the sum of an angle and its supplement is $180^\circ$. So, $x+(x - 76)=180$.

Step3: Solve the equation

Simplify the left - hand side: $2x-76 = 180$.
Add $76$ to both sides: $2x=180 + 76=256$.
Divide both sides by $2$: $x=\frac{256}{2}=128$.

Step4: Find the supplement

The supplement is $x - 76=128 - 76 = 52$.

Answer:

measure of the angle = $128^\circ$, measure of the angle's supplement = $52^\circ$