如图，已知∠BOC=2∠AOC，OD平分∠AOB，且∠COD=20°，求∠AOB的度数

显示全部楼层 · 2012-1-7 11:33:22

解：∵∠BOC＝2∠AOC∴∠AOB＝∠AOC+∠BOC＝∠AOC+2∠AOC＝3∠AOC∵OD平分∠AOB∴∠AOD＝∠AOB/2＝3∠AOC/2∴∠COD＝∠AOD-∠AOC＝3∠AOC/2-∠AOC＝∠AOC/2∵∠COD＝20°∴∠AOC/2＝20°∴∠AOC＝40°∴∠AOB＝3∠AOC＝120°...

千问 · 2012-1-7 11:33:22

∵∠BOC＝2∠AOC∴∠AOB＝∠AOC+∠BOC＝∠AOC+2∠AOC＝3∠AOC∵OD平分∠AOB∴∠AOD＝∠AOB/2＝3∠AOC/2∴∠COD＝∠AOD-∠AOC＝3∠AOC/2-∠AOC＝∠AOC/2∵∠COD＝20°∴∠AOC/2＝20°∴∠AOC＝40°∴∠AOB＝3∠AOC＝120°...

千问 · 2012-1-7 11:33:22

∵∠BOC＝2∠AOC∴∠AOB＝∠AOC+∠BOC＝∠AOC+2∠AOC＝3∠AOC∵OD平分∠AOB∴∠AOD＝∠AOB/2＝3∠AOC/2∴∠COD＝∠AOD-∠AOC＝3∠AOC/2-∠AOC＝∠AOC/2∵∠COD＝20°∴∠AOC/2＝20°∴∠AOC＝40°∴∠AOB＝3∠AOC＝120°...

千问 · 2012-1-7 11:33:22

解：∵∠BOC＝2∠AOC∴∠AOB＝∠AOC+∠BOC＝∠AOC+2∠AOC＝3∠AOC∵OD平分∠AOB∴∠AOD＝∠AOB/2＝3∠AOC/2∴∠COD＝∠AOD-∠AOC＝3∠AOC/2-∠AOC＝∠AOC/2∵∠COD＝20°∴∠AOC/2＝20°∴∠AOC＝40°∴∠AOB＝3∠AOC＝120°...