In the given circle with center O, angle AOB = 30 degrees. Find the value of x (angle ACB).

1. Identify the given information:

• Central angle AOB = 30 degrees.
• Angle x (ACB) 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 AB is 30 degrees.

3. Relate inscribed angle to intercepted arc:

• The inscribed angle ACB subtends the arc AB.
• 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 AB
• x = (1/2) * 30 degrees
• x = 15 degrees.

Ответ: 15°