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.
180-x = x-76
x = 128
180-x = 52
To find the measures of the angle and its supplement, we can set up an equation based on the given information. Let's denote the measure of the angle as x.
According to the problem, the measure of the angle's supplement is 76° less than the measure of the angle. The measure of the supplement is therefore x - 76°.
The sum of an angle and its supplement is always 180°. So, we can set up the following equation:
x + (x - 76°) = 180°
Simplifying the equation, we get:
2x - 76° = 180°
Now, let's solve for x:
2x = 180° + 76°
2x = 256°
x = 256° / 2
x = 128°
Hence, the measure of the angle is 128°, and its supplement is:
x - 76° = 128° - 76°
x - 76° = 52°
Therefore, the measure of the angle is 128°, and its supplement is 52°.