Assessment and Learning in Knowledge Spaces (ALEKS) Practice Exam

What is the term for an angle whose vertex is located at the center of a circle?

1. Central Angle

2. Inscribed Angle

3. Reflex Angle

4. Acute Angle

The correct answer is: Central Angle

A central angle is defined as an angle whose vertex is positioned at the center of a circle, with its sides (or arms) extending out to the circumference. This type of angle directly relates to the arc that it intercepts within the circle. The measure of the central angle in degrees is equal to the arc length it subtends at the circle. In contrast, the other angle types do not share this specific characteristic. An inscribed angle has its vertex on the circumference of the circle and opens toward the interior of the circle. A reflex angle is defined as an angle larger than 180 degrees but less than 360 degrees, regardless of its position related to a circle. An acute angle is any angle that measures less than 90 degrees, which again is unrelated to its position in a circle. Therefore, a central angle uniquely describes the relationship between the vertex at the circle's center and the intercepted arc, making it the correct answer in this context.