To find the central angle of a circle, you need to identify two radii that extend from the center of the circle to its circumference, creating a wedge-shaped section. The following steps will help you determine the central angle:
- Understand the Definition: A central angle is an angle whose vertex is at the center of the circle and whose sides (or rays) extend to the circle’s edge.
- Measure the Arc: If you have the arc length (the distance along the circumference between two points on the circle), you can calculate the central angle using the formula:
Central Angle (in degrees) = (Arc Length / Circumference) × 360. - Use the Circle’s Radius: Alternatively, if you know the radius of the circle, the formula for the circumference is
C = 2πr. Substitute the radius into this formula to find the circumference before applying it in the central angle calculation. - Inscribed Angles: If two points on the circumference are given, you can also use inscribed angle relationships, where the central angle is twice the inscribed angle that subtends the same arc.
By applying these methods, you can accurately determine the central angle for any given circle.