Central angle
A central angle is an angle whose vertex is at the center of a circle. It is formed by two radii (plural of radius) that extend from the center to the endpoints of an arc. The measure of a central angle is equal to the measure of the subtended arc.

Explanation:
To understand the concept of a central angle, let's first revisit some basic terms related to circles.

Circle:
A circle is a closed curved shape in which all points on the circumference are equidistant from the center. It is made up of various parts, such as the center, radius, diameter, circumference, and arcs.

Center:
The center is the point within a circle that is equidistant from all points on the circumference.

Radius:
A radius is a line segment that connects the center of a circle to any point on its circumference. It is the distance between the center and any point on the circle.

Central Angle:
A central angle is an angle formed by two radii that extend from the center of a circle to the endpoints of an arc. It is named so because its vertex is located at the center of the circle.

Properties of a Central Angle:
1. The measure of a central angle is equal to the measure of the subtended arc. In other words, if we measure the arc that the central angle "cuts out" from the circumference of the circle, it will have the same measure as the central angle itself.
2. The sum of the measures of all central angles in a circle is 360 degrees. This is because the circumference of a circle is divided into 360 degrees.

Example:
Let's consider a circle with center O. Suppose we draw two radii OA and OB that extend to the endpoints of an arc AB. The angle AOB, formed by these radii, is a central angle. Its measure is equal to the measure of arc AB.

Conclusion:
In conclusion, any angle whose vertex is at the center of a circle is called a central angle. It is formed by two radii that extend from the center to the endpoints of an arc. The measure of a central angle is equal to the measure of the subtended arc.

Central Angle