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.
    • example of Central Angle

Video Examples: Inscribed and Central Angles


Solved Example onCentral Angle

Ques: 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?

    example of Central Angle
    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.

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