The central angle of a circle formula calculates the angle between two radii of a circle. A central angle can also be defined as an angle subtended by the arc of a circle at the center of the circle. The radius vectors form the arms of the central angle. Let us understand the central angle of a circle formula using solved examples.
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To calculate the central angle using the central angle formula, we require the measure of the arc length that subtends the central angle at the center and the radius of the circle. The central angle of a circle formula is given as,
Central angle, θ = (Arc length × 360º)/(2πr) degrees
Central angle, θ = Arc length/r radians
where r is the radius of the circle.
Let us see how to use the central angle formula in the following solved examples section.
Solved Examples Using Central Angle of a Circle Formula
Example 1:Find the central angle, where the arc length measurement is about 30 units and the length of the radius is 15 units.