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In the diagram below, $\angle AOB = 99^{\circ}$, and $\angle AOC = 133^{\circ}.$ What is the measure of $\angle BOC$?

Feb 4, 2021

The angles around vertex $O$ sum to $360^{\circ}$, so we have $\angle AOB+\angle BOC+\angle AOC = 360^{\circ}.$In particular, \begin{align*} \angle BOC &= 360^{\circ} - \angle AOB - \angle AOC \\ &= 360^{\circ} - 99^{\circ} - 133^{\circ} \\ &= \boxed{128^{\circ}}. \end{align*}