## Central Angle of a circle

### In geometry, a central angle is an angle formed by two radii (plural of radius) of a circle, with its vertex at the center of the circle

In geometry, a central angle is an angle formed by two radii (plural of radius) of a circle, with its vertex at the center of the circle. In other words, a central angle is an angle whose initial and terminal sides are two radii of the circle.

The degree measure of a central angle is equal to the measure of the arc intercepted by the angle at the center of the circle. By convention, we use degrees to measure angles, so a central angle can have a measure in degrees.

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

Measure of central angle = (Arc length / Circumference) * 360°

where the arc length is the length of the arc intercepted by the central angle, and the circumference is the distance around the circle.

For example, let’s say we have a circle with a circumference of 20 meters. If the arc length intercepted by a central angle is 5 meters, we can calculate the measure of the central angle as:

Measure of central angle = (5 / 20) * 360°

Measure of central angle = 0.25 * 360°

Measure of central angle = 90°

So, in this example, the central angle would measure 90 degrees.

Central angles have several important properties and applications in geometry, trigonometry, and calculus. They are used to calculate arc lengths, find areas of sectors, and solve problems related to circles in various contexts.

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