Arc Addition Theorem

Start by drawing the radii $\overline{PA},$ $\overline{PB},$ and $\overline{PC},$ and by labeling the central angles corresponding to $\overgroup{AB},$ $\overgroup{BC},$ and $\overgroup{ABC}.$

By definition, the arc measure is equal to the measure of the related central angle. By the Angle Addition Postulate, $m\angle 3$ can be written as the sum of $m\angle 1$ and $m\angle 2.$ Finally, in the above formula, $m\overgroup{AB}$ and $m\overgroup{BC}$ can be substituted for $m\angle 1$ and $m\angle 2,$ respectively.