We know that when arcs are congruent, they have congruent central angles.
Work Step by Step
An arc takes up a certain portion of a given circle. Just like we can related the percentage of a pizza that is eaten to the number of slices (each slice has an arc equal to 1/8 the circumference of the circle), we can relate the angle to the percentage of the circle that the arc takes up. Thus, because congruent arcs take up the same amount of the circle, congruent arcs correspond to congruent central angles.