Question

如图，OD平分∠BOC，,OE平分∠AOC，请求出∠DOC和∠AOE的度数，并判断∠DOE与∠AOB是否互补，并说明理由

（∠BOC=70°） ∠AOC=50°

Answer 1

∵OD平分∠BOC，,OE平分∠AOC
∴∠DOC=1/2∠BOC=1/2×70°=35°
∠AOE=1/2∠AOC=1/2×50°=25°
∵∠COE=∠AOE=25°
∴∠DOE=∠DOC+∠COE=35°+25°=60°
∵∠AOB=∠OC+∠BOC=50°+70°=120°
∴∠AOB+∠DOE=60°+120°=180°
∴∠DOE与∠AOB互补

Answer 2

∵OD平分∠BOC，,OE平分∠AOC
∴∠DOC=1/2∠BOC=1/2×70°=35°
∠AOE=1/2∠AOC=1/2×50°=25°
∵∠COE=∠AOE=25°
∴∠DOE=∠DOC+∠COE=35°+25°=60°
∵∠AOB=∠OC+∠BOC=50°+70°=120°
∴∠AOB+∠DOE=60°+120°=180°
∴∠DOE与∠AOB互补

Answer 3

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