Geometry Essentials · Superchallenge problem

Ten rays $OR_1, OR_2, \ldots, OR_{10}$ are drawn in that order from point $O$, all on the same side of line $OR_1$, so that each of the nine angles $\angle R_1OR_2, \angle R_2OR_3, \ldots, \angle R_9OR_{10}$ measures $10^\circ$. Every pair of the rays forms an angle, $45$ angles in all. Find the sum of the measures of all $45$ angles, in degrees.