# central angle

**Definition of Central Angle**

- The angle in a circle whose vertex is the center of the circle is called the Central Angle.

**Example of Central Angle**

- In the figure shown, O is the center of the circle and angle POQ is the central angle.

**Solved Example on Central Angle**

A circle is divided into 4 congruent sectors and then each of them is divided into 3 congruent sectors as in the figure. What is the measure of the central angle POQ in degrees?

**Choices:**

A. 45

B. 30

C. 90

D. 60

**Correct Answer: D **

**Solution:**

**Step 1:** Central angle of each sector = (360/12)° = 30°

**Step 2:** Measure of the central angle POQ is 2(30) = 60.

**Related Terms for Central Angle**