Question

如图,∠COB=2∠AOC,OD平分∠AOB,且∠COD=19°,求∠AOB

Answer 1

∵∠COB＝2∠AOC

∴∠AOB＝∠AOC+∠BOC＝3∠AOC

∵OD平分∠AOB

∴∠AOD＝1/2∠AOB＝3/2∠AOC

∴∠COD＝∠AOD-∠AOC＝3/2∠AOC-∠AOC＝1/2∠AOC

∵∠COD＝19

∴1/2∠AOC＝19

∴∠AOC＝38

∴∠AOB＝3∠AOC＝114°

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