$$\angle AOF = 30^\circ$$, $$\angle BOE = 40^\circ$$
$$\angle FOD = \angle BOE = 40^\circ$$ (как вертикальные)
$$\angle AOC = 180^\circ - \angle AOF - \angle FOD = 180^\circ - 30^\circ - 40^\circ = 110^\circ$$
Ответ: $$\angle AOC = 110^\circ$$