Using vertical angles to determine the measure of a minor arc for a circle

The video tutorial discusses a geometry problem involving central angles and minor arcs. The teacher explains that the central angle is unknown and demonstrates how to use the concept of vertical angles to find the solution. The tutorial emphasizes the importance of understanding congruent angles when lines intersect and how this knowledge can be applied to solve problems involving arcs and angles.

Why is it important to know the measure of the central angle when dealing with arcs?

In the example discussed, how was the measure of the minor arc determined?