Finding the Measure of a Central Angle in a Circle | Formula and Example Calculation

central angle of a circle

The central angle of a circle is an angle formed by two radii (plural for radius) that connect the center of the circle to any two points on its circumference

The central angle of a circle is an angle formed by two radii (plural for radius) that connect the center of the circle to any two points on its circumference. The measure of the central angle is always taken with respect to the center of the circle, and it is typically expressed in degrees or radians.

To find the measure of a central angle, you can use the formula:

Angle Measure = (Arc Length / Circumference) * 360 degrees

Where:
– Arc Length refers to the length of the arc intercepted by the central angle on the circumference of the circle, measured in the same units as the circumference.
– Circumference is the distance around the entire circle.

For example, if you have a circle with a circumference of 10 cm and an arc length of 2 cm intercepted by a central angle, you can calculate the angle measure as:

Angle Measure = (2 cm / 10 cm) * 360 degrees
Angle Measure = 0.2 * 360 degrees
Angle Measure = 72 degrees

Hence, the measure of the central angle in this case is 72 degrees.

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