The measure of one angle is 32° less than the measure of its supplement. Write an equation and solve it to find the measurements of the angles.

Let's make variables for two angles first. One angle will be x, and the other will be y.

Since they're supplementary, we know x + y = 180

We also know x = y - 32, since it's 32 degrees less than it's supplement.

Input the value of x into the first equation and ...

y - 32 + y = 180

2y - 32 = 180

Add 32 to both sides:

2y = 212

Divide both sides by 2:

y = 106

We can solve for x in two ways.

One, we can subtract 32 from 106 since x is 32 degrees less.

Or, we could also just subtract 106 from 180 since we know the angles are supplementary.

x = 74

74 degrees and 106 degrees. The equation is y - 32 + y = 180, or x + y = 180