Question

An angle measures 160° more than the measure of a supplementary angle. What is the measure of each angle?

Answer 1

The two supplementary angles are `10` and `170` degrees.

Explanation:

Two angles are supplementary when that add up to `180` degrees. In this case, we are given that one of the two angles is `160` degrees more than the other. We can construct the following equation.

`x+(x+160)=180`

`x` represents the degree measure of the smaller angle. Now, all we need to do is solve the equation for `x`.

`2x+160=180`

`2x=20`

`x=10`

Now that we have the value of the smaller angle, we can easily solve for the larger angle. We are told that it is `160` degrees larger than the other one.

`10+160=170`

Therefore, the two supplementary angles are `10` and `170` degrees.