One of the adjacent angles is 72 degrees larger than the other. What is the degree measure of the smaller of the angles.

Given:
angle AOB and angle BOС are adjacent (they have a common side ВO),
angle AOB – angle BOS = 72 degrees.
Find the degree measures of the angle AOB and angle BOC -?
Decision:
Consider the adjacent corners AOB and BOС.
Let the degree measure of the AOB angle be x degrees, then the degree measure of the AOB angle is (x + 72) degrees. We know that the sum of the degree measures of adjacent angles is 180 degrees. Let’s make the equation:
x + x + 72 = 180;
x + x = 180 – 72;
x + x = 108;
x * (1 + 1) = 108;
x * 2 = 108;
x = 108: 2;
x = 54 degrees – the degree measure of the ВOC angle;
54 + 72 = 126 degrees is the degree measure of the AOB angle.
Answer: 54 degrees; 126 degrees.