Which angle is defined as having its vertex at the center of a circle?

Which angle is defined as having its vertex at the center of a circle?

• A. Central angle
• B. Inscribed angle
• C. Reflex angle
• D. Exterior angle

Answer: (A)

A central angle is defined as an angle whose vertex is located at the center of a circle, and its sides (or rays) extend out to the circumference of the circle. This definition is foundational in understanding various concepts in circle geometry. In the context of circles, a central angle directly relates to the arcs it intercepts. For instance, the measure of a central angle is equal to the measure of the arc that it subtends. This property makes central angles particularly significant in circle theorem discussions and applications. The other types of angles mentioned do not fit this definition. An inscribed angle, for example, has its vertex on the circle itself, whereas a reflex angle is greater than 180 degrees and does not have a specific relationship to circles. An exterior angle is one that is outside a polygon or circle and does not concern the angle's vertex being at the center of the circle. Thus, the definition and associated properties of a central angle provide the correct answer in this scenario.

A central angle is defined as an angle whose vertex is located at the center of a circle, and its sides (or rays) extend out to the circumference of the circle. This definition is foundational in understanding various concepts in circle geometry.

In the context of circles, a central angle directly relates to the arcs it intercepts. For instance, the measure of a central angle is equal to the measure of the arc that it subtends. This property makes central angles particularly significant in circle theorem discussions and applications.

The other types of angles mentioned do not fit this definition. An inscribed angle, for example, has its vertex on the circle itself, whereas a reflex angle is greater than 180 degrees and does not have a specific relationship to circles. An exterior angle is one that is outside a polygon or circle and does not concern the angle's vertex being at the center of the circle. Thus, the definition and associated properties of a central angle provide the correct answer in this scenario.