A sprinter runs the curve of this $200$ m in $13\mathrm{.}95$ s$.$ Assume he ran in a lane which makes a semicircle $($r $=35\mathrm{.}9$ m$)$ for the first part of the race. At $4\mathrm{.}09$ s into the race his speed is $6\mathrm{.}1$ m$/$s$.$ At $7\mathrm{.}1$ s into the race his speed is $8\mathrm{.}7$ m$/$s$.$ His speed after the curve was $12\mathrm{.}1$ m$/$s$.$

What was the sprinter's average angular velocity at $13\mathrm{.}95$ s$?$ Answer in deg$/$s$.$