The OC beam divides the extended angle AOB into two angles so that the AOC angle is 50 degrees greater than the BOC angle.

The OC beam divides the extended angle AOB into two angles so that the AOC angle is 50 degrees greater than the BOC angle. Find the degree measures of the AOC and BOC angles.

1. The expanded angle is 180⁰.

Let the AOC angle be equal to x⁰, then the degree measure of the AOC angle is (x + 50) ⁰.

2. Let us find the degree measure of the angle AOB by adding the degree measures of the angles AOC and BOC.

(x + x + 50), and according to the condition of the AOB unfolded angle, it means equal to 180⁰.

3. Let’s compose and solve the equation.

x + x + 50 = 180;

2x + 50 = 180;

2x = 180 – 50;

2x = 130;

x = 130/2;

x = 65⁰ is the degree measure of the AOC angle, then the degree measure of the AOC angle is 65 + 50 = 115⁰.

Answer: 65⁰; 115⁰.