Central angle, as the name suggests is an angle made at the center. Central angles are formed by the hour, minute and seconds hand of a traditional clock. Indeed the three hands make three central angle at instant of time, each angle formed by any two hands of the clock.

Central Angle

Central angle is an important geometric idea based on which many other concepts are defined and theorems proved. Let us look how the central angle is defined and how it is used in solving geometric problems.

A Central angle is an angle formed at the center of a circle by two radii of the circle. Thus the center the circle is the vertex of the angle and the radii the sides of the angle. If θ is the measure of a central angle then 0º ≤ θ ≤ 180º.

Central Angle Definition

In the above diagram the central angle AOB is made by the radii OA and OB of the circle O at the center. When the two radii coincide the measure of the central angle = 0º and if they form opposite rays, then the measure of central angle = 180º.
The sum of measures of central angles of a circle which contain no common point between them = 360º, as they all together describe the circle.

Definition of Central Angle
In the above diagram, the angles 1, 2, 3 and 4 share the common vertex at the center and they do not share any other common point.
m ∠1 + m ∠2 + m ∠3 + m ∠4 = 360º.