Two lines AB and CD intersect at O. Ray OE is the bisector of angle BOD. If angle AOC = 70°, find angle COE (where E lies in the region of angle BOD).

Angle BOD is vertically opposite angle AOC, so angle BOD = 70°. OE bisects it, so angle BOE = 35°. Angle COB is a linear pair with angle AOC, so angle COB = 180 - 70 = 110°. Then angle COE = angle COB + angle BOE = 110 + 35 = 145°.