The swept angle ABC is divided into two angles by the ray BO. The ABO is 50 ° less than the OBC.

The swept angle ABC is divided into two angles by the ray BO. The ABO is 50 ° less than the OBC. Calculate the degree measures of the angles ABO and OBC.

1. Let’s denote the degree measure of the angle ABO through x.

2. Determine the degree measure of the OBC angle:

(x + 50˚).

3. Since the degree measure of the expanded angle is 180˚, we compose and solve the equation:

(x + 50˚) + x = 180˚;

x + 50˚ + x = 180˚;

2x + 50˚ = 180˚;

2x = 180˚ – 50˚;

2x = 130˚;

x = 130˚: 2;

x = 65˚.

4. The degree measure of the ABO angle is x = 65˚.

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

x + 50˚ = 65˚ + 50˚ = 115˚.

Answer: the degree measure of the ABO angle is 65˚, the degree measure of the OBC angle is 115˚.