Use an algebraic equation to find the measures of the two angles described below. begin by letting x represent the degree measure of the angle's supplement. the measure of the angle is eight times greater than its supplement. what is the measure of the supplement?

Two angles are said to be supplement when their measure add up to 180 degrees.

Assume that the angle we are looking for is a and its supplement is s (I used s instead of x).

a + s = 180
a = 180 - s > equation I

We know that the measure of the angle is eight times greater than its supplement.
This means that:
a = 8s > equation II

Substitute by equation II in equation I to get s as follows:
180 - s = 8s
180 = 9s
s = 20 degrees

Substitute in equation I to get the measure of the angle as follows:
a = 180 - s = 180 - 20 = 160 degrees

Based on these calculations:
The measure of the angle is 160 degrees
The measure of its supplement is 20 degrees