Question

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?

Answer 1

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