如图,直线AB、CD相交于点O,OE平分∠BOD,OF平分∠COE,∠AOD:∠BOE=7:1,求∠AOF的度数.

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如图,直线AB、CD相交于点O,OE平分∠BOD,OF平分∠COE,∠AOD:∠BOE=7:1,求∠AOF的度数.
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如图,直线AB、CD相交于点O,OE平分∠BOD,OF平分∠COE,∠AOD:∠BOE=7:1,求∠AOF的度数.
如图,直线AB、CD相交于点O,OE平分∠BOD,OF平分∠COE,∠AOD:∠BOE=7:1,求∠AOF的度数.

如图,直线AB、CD相交于点O,OE平分∠BOD,OF平分∠COE,∠AOD:∠BOE=7:1,求∠AOF的度数.

∵OE平分∠BOD
∴∠BOE=∠DOE
∵∠AOD:∠BOE=7:1
∴∠AOD=7∠BOE
∵∠AOD+∠DOE+∠BOE=∠AOB=180
∴7∠BOE+∠BOE+∠BOE=180
∴∠BOE=20
∴∠DOE=∠BOE=20
∴∠COE=∠COD-∠DOE=180-20=160
∴∠BOD=∠BOE+∠DOE=2∠BOE=40
∵∠AOC与∠BOD为对顶角
∴∠AOC=∠BOD=40
∵OF平分∠COE
∴∠COF=∠COE/2=160/2=80
∴∠AOF=∠AOC+∠COF=40+80=120°