In the given circle with center O, angle AOC = 120 degrees. Find the value of x (angle ABC).

1. Identify the given information:

• Central angle AOC = 120 degrees.
• Angle x (ABC) is an inscribed angle.

2. Relate central angle to intercepted arc:

• The measure of a central angle is equal to the measure of its intercepted arc. Thus, the measure of arc AC is 120 degrees.

3. Relate inscribed angle to intercepted arc:

• The inscribed angle ABC subtends the arc AC.
• The measure of an inscribed angle is half the measure of its intercepted arc.

4. Calculate the inscribed angle x:

• x = (1/2) * measure of arc AC
• x = (1/2) * 120 degrees
• x = 60 degrees.

Ответ: 60°