Find adjacent angles if one is 138 ° smaller than the other.

1. Let us denote the degree measure of the smaller of the adjacent angles by x.

2. Determine the degree measure of the larger angle:

(x + 138˚).

3. Since the sum of adjacent angles is 180˚, compose and solve the equation:

(x + 138˚) + x = 180˚;

x + 138˚ + x = 180˚;

2x + 138˚ = 180˚;

2x = 180˚ – 138˚;

2x = 42˚;

x = 42˚: 2;

x = 21˚.

4. The degree measure of the smaller of the adjacent angles is x = 21˚.

5. What is the degree measure of the larger angle?

x + 138˚ = 21˚ + 138˚ = 159˚.

Answer: the degree of the smaller angle is 21˚, the degree of the larger angle is 159˚.