Final answer:
The name of the central angle associated with arc (ABC) is a Central Angle, which is subtended by an arc between two points on the circle that the radii intersect.
Step-by-step explanation:
The name of the central angle that is associated with the following arc (ABC) is A) Central Angle. In a circle, a central angle is an angle whose apex (vertex) is the center of the circle, and whose sides (legs) are radii that intersect the circle at two points, creating an arc between those points. This arc is the one referred to in the question, denoted by (ABC).
Since every point on a spinning wheel travels through the same angle of rotation during a rotation, the point near the outer edge will trace a longer arc while the point near the center traces a smaller arc. However, the central angle they subtend will be the same. This is because the arc length that corresponds to a given angle is directly proportional to the radius of the circle, such that the arc length for a given central angle increases with a larger radius.
Therefore, when visualizing ▲ABC as a slice of a bigger circle, the baseline length is approximately equivalent to the arc length of the 'slice' created by that central angle, consistent with the relationship between angle of rotation and arc length in a circle.