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
    A. 45
    B. 30
    C. 90
    D. 60
    Correct Answer: D


    Step 1: Central angle of each sector = (360/12) = 30
    Step 2: Measure of the central angle POQ is 2(30) = 60.