Question

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. ​

Answer 1

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