如图, 已知 $\angle A O B=30^{\circ}, \angle A O E=140^{\circ}, O B$ 平分 $\angle A O C, O D$ 平分 $\angle A O E$.

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(1) 求 $\angle A O C$ 的度数.

(2) 求 $\angle C O D$ 的度数.
(1) 解: $\because \angle \mathrm{AOB}=30^{\circ}, \mathrm{OB}$ 平分 $\angle \mathrm{AOC}$

$\therefore \angle \mathrm{AOC}=2 \angle \mathrm{AOB}=2 \times 30^{\circ}=60^{\circ}$

(2) 解: $\because \angle \mathrm{AOE}=140^{\circ}, \angle \mathrm{AOC}=60^{\circ}$

$\therefore \angle \mathrm{COE}=\angle \mathrm{AOE}-\angle \mathrm{AOC}=140^{\circ}-60^{\circ}=80^{\circ}$

又 $\because \mathrm{OD}$ 平分 $\angle \mathrm{AOE}$

$\therefore \angle \mathrm{DOE}=\frac{1}{2} \angle \mathrm{AOE}=\frac{1}{2} \times 140^{\circ}=70^{\circ}$

$\therefore \angle \mathrm{COD}=\angle \mathrm{COE}-\angle \mathrm{DOE}=80^{\circ}-70^{\circ}=10^{\circ}$