Geometry Essentials · Superchallenge problem

Rays $OA$, $OB$, $OC$ are drawn with $m\angle AOB = 150^\circ$ and $m\angle BOC = 110^\circ$. Ray $OM$ bisects $\angle AOB$ and ray $ON$ bisects $\angle BOC$. Ray $OC$ may lie on either side of line $OB$. Find the sum of all possible values of $m\angle MON$.