Question

An angle measures 67.2° less than the measure of a supplementary angle. What is the measure of each angle?

Answer 1

Two supplementary angles always adds up to 180 degrees. If an angle is 67.2 degrees less than the measure of a supplementary angle, an equation can be formed where "A" represents the larger angle, and (A - 67.2) represents the smaller angle.

(A - 67.2)+A=180

(Combine the A's)

2A - 67.2=180

(Add 67.2 to both sides)

2A = 247.2

(Divide by 2 to both sides)

A = 123.6

123.6 degrees is the larger angle.

The smaller angle is represented by (A - 67.2). We now know the value of A so lets plug it in. (123.6 - 67.2) = 56.4. 56.4 is the value of the smaller angle.

We can double check to make sure we got the right answer.

123.6 + 56.4 = 180