Geometry Essentials · Superchallenge problem

Rays $OA$, $OB$, $OC$, $OD$ are drawn in that order with $m\angle AOD = 150^\circ$ (rays $OB$ and $OC$ lie inside $\angle AOD$). The bisector of $\angle AOB$ and the bisector of $\angle COD$ form an angle of $110^\circ$. Find the measure of the angle formed by the bisector of $\angle AOC$ and the bisector of $\angle BOD$.