Angle DOC is a vertical angle to AOB. Since this is a central angle, arc AB is 50.
Angles AOE, EOD, and DOC are supplementary. 180 - 60 - 50 = 70. Angle AOE is also central, so arc AE is 70.
All arcs combined add to 360, so 360 - 70 - 50 = 240 (we subtracted every other arc besides ECB, which is 240.)
We know angle BOC is vertical to the sum of AOE and EOD, so 60+ 70 = 130. Angle BOC is 130.
