an angle with the vertex at the center of the circle and with sides forming radii of the circle

An angle in a circle between two radii.

An angle with the vertex at the center of the Earth, with one ray passing through the hypocenter (and also the epicenter) and the other ray passing through the recording station.

an angle that has its vertex at the center of a circle.

An angle whose vertex is at the center of a circle and whose sides contain radii of the circle.

A central angle is an angle whose vertex is the center of a circle, and whose sides pass through a pair of points on the circle, thereby subtending an arc between those two points whose angle is (by definition) equal to the central angle itself. It is also known as the arc segment's angular distance.