Question

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Answer 1

1. 因为OD 是 ∠AOB 的角平分线，则 ∠AOD = ∠BOD = 1/2∠AOB

2. 又因为 OE 是 ∠BOD 的角平分线，则 ∠BOC = ∠COD = 1/2∠BOD = 1/4∠AOB

3. ∠DOE = 1/3∠AOE，那么 ∠AOE = 3∠DOE，∠AOD = ∠AOE + ∠DOE = 4∠DOE。所以，∠DOE = 1/4∠AOD = 1/8∠AOB

4. ∠COE = ∠DOE + ∠COD = 1/8∠AOB + 1/4∠AOB = 3/8∠AOB = 45°

   所以，∠AOB = 45° ÷ (3/8) = 120°

Answer 2