Assessment and Learning in Knowledge Spaces (ALEKS) Practice Exam

What defines an angle that subtends an arc at the center of the circle?

1. Central Angle

2. Inscribed Angle

3. Reflex Angle

4. Obtuse Angle

The correct answer is: Central Angle

An angle that subtends an arc at the center of a circle is known as a central angle. This type of angle is formed by two radii of the circle that extend from the center to the endpoints of the arc. The measurement of the central angle is directly related to the length of the arc it subtends, meaning the larger the arc, the greater the central angle. This relationship is fundamental in circle geometry, as it allows for various calculations involving the circle's properties, such as circumference and sector areas. In contrast, other types of angles like inscribed angles are defined differently, as they are formed by two chords in the circle that share an endpoint on the circumference. Reflex angles and obtuse angles pertain to measures beyond the 90-degree mark, often involving angles that are not specifically related to the subtended arcs in circle geometry. Therefore, the identification of the angle that directly relates to the arc at the center of the circle precisely defines it as a central angle.