Assessment and Learning in Knowledge Spaces (ALEKS) Practice Exam

A central angle creates which type of shape within the circle?

1. Sector

2. Arc

3. Segment

4. Triangle

The correct answer is: Sector

A central angle creates a sector within a circle. A sector is defined as a portion of a circle that is enclosed by two radii and the arc that lies between them. When you consider a central angle, it is formed at the center of the circle and the two rays extend outward to intersect the circle's circumference, delineating the space that is encompassed by those two radii and the arc connecting their endpoints. The other options do not accurately describe the geometric shape formed by a central angle. An arc is merely the curved line segment that forms part of the circle between the two points, while a segment refers to the area bounded by a chord and the corresponding arc, which does not include the center. A triangle would involve three points, and while it could be formed with a central angle by connecting the endpoints of the arc to the center, it is not the primary shape directly associated with a central angle. Therefore, the most accurate answer to the question about the shape created by a central angle is a sector.