The angle in a circle whose vertex is the center of the circle is called the central angle.
Examples 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 it 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
