Mathematics

The key insight is that in a circle, the central angle and its intercepted arc have equal measures—this is the fundamental definition of how we measure arcs in degrees. Since $\angle AOB$ is the central angle (the angle at the center $O$ formed by radii $OA$ and $OB$), the arc it intercepts has exactly the same degree measure. The minor arc is simply the shorter path along the circle between $A$ and $B$, which corresponds to this central angle.

The key insight is that in a circle, the central angle and its intercepted arc have equal measures—this is the fundamental definition of how we measure arcs in degrees. Since $\angle AOB$ is the central angle (the angle at the center $O$ formed by radii $OA$ and $OB$), the arc it intercepts has exactly the same degree measure. The minor arc is simply the shorter path along the circle between $A$ and $B$, which corresponds to this central angle.