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: Define variables

Let the measure of the angle be $x$. Then its supplement is $180^\circ - x$.

Step2: Set up equation

Given that the supplement is $76^\circ$ less than the angle, so $180 - x = x - 76$.

Step3: Solve for x

Add $x$ to both sides: $180 = 2x - 76$.
Add $76$ to both sides: $256 = 2x$.
Divide by $2$: $x = 128^\circ$.

Step4: Find supplement

Supplement is $180 - 128 = 52^\circ$. Wait, no—wait, correction: Wait, the problem says "the measure of an angle’s supplement is 76° less than the measure of the angle". So supplement = angle - 76. So angle + supplement = 180. Let angle = $x$, supplement = $x - 76$. Then $x + (x - 76) = 180$.
$2x - 76 = 180$
$2x = 180 + 76 = 256$
$x = 128^\circ$ (angle), supplement = $128 - 76 = 52^\circ$? Wait, no, that can't be. Wait, supplement should be larger? Wait, no—if supplement is less than the angle, then angle is larger. Wait, let's check: If angle is 128, supplement is 52. 52 is 76 less than 128 (128 - 52 = 76). Yes, that's correct. Wait, but usually supplements add to 180. 128 + 52 = 180. Correct. So angle is 128°, supplement is 52°? Wait, no, wait the problem says "the measure of an angle’s supplement is 76° less than the measure of the angle". So supplement = angle - 76. So angle + (angle - 76) = 180. So 2 angle = 180 + 76 = 256. Angle = 128. Supplement = 128 - 76 = 52. Yes.

Answer:

Measure of the angle = $128^\circ$
Measure of the angle’s supplement = $52^\circ$