What is the measure of AC (the minor arc)?

Answer:-  124°, Option A is the correct answer.

The measure of the minor arc AC is 124°.

An inscribed angle is an angle that has its vertex on the circle and its sides are chords of the circle. The measure of an inscribed angle is always half the measure of the arc that it intercepts. In this case, the inscribed angle is 62°, so the measure of the arc that it intercepts, AC, is 2 * 62° = 124°.