Geometry Essentials · Medium problem

Rays $\overrightarrow{OA}$, $\overrightarrow{OB}$, $\overrightarrow{OC}$, $\overrightarrow{OD}$ leave point $O$ with $A$, $B$, $C$, $D$ in order. The three angles $\angle AOB$, $\angle BOC$, $\angle COD$ are three consecutive multiples of $5$, and $m\angle AOD = 90^\circ$. Find the three angles and $m\angle BOD$.