Answer:
See below.
Explanation:
Central angles AOB and DOC are vertical angles, so they are congruent.
m<AOB = 50°
BD is a diameter, so the measure of central angle BOD is 180°.
The measure of an arc of a circle is equal to the measure of the central angle that subtends it.
m<AOB + m<AOE + m<EOD = 180°
50° + m<AOE + 60° = 180°
m<AOE + 110° = 180°
m<AOE = 70°
m(arc)AE = m<AOE = 70°
m(arc)AB = m<AOM = 50°
A full circle has 360 deg of central angle and of arc measure.
m(arc)ECB = 360° - m(arc)AE - m(arc)AB
m(arc)ECB = 360° - 70° - 50°
m(arc)ECB = 240°
Angle BOC is vertical with angle AOD.
m<BOC = m<AOD = m<AOE + m<EOD
m<BOC = 70° + 60°
m<BOC = 130°