Question

如图,已知∠DOE=70°,OD平分∠AOB,OE平分∠BOC,求∠AOC

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写上步骤

Answer 1

∵OD平分∠AOB,OE平分∠BOC
∴∠BOD=1/2∠AOB
∠BOE=1/2∠BOC
∴∠DOE=∠BOD+∠BOE=1/2∠AOB+1/2∠BOC=1/2∠AOC
∴∠AOC=2∠DOE=2×70°=140°

Answer 2

设coe=x
则eob=x
dob=70+x=doa
doc=doe-coe=70-x
aoc=aod+doc=70+x+70-x=140

Answer 3

140°

追问

怎么算

追答

∠DOB=1/2∠AOB，∠BOE=1/2∠BOC
∴∠AOC=∠AOB+∠BOC=2(∠DOB+∠BOE)
=2*70°=140°