Question

直线AB交CD于O点OE平分∠BOD,OF平分∠COB,∠AOD:∠BOE=4:1,求∠AOF的度数

Answer 1

∠AOD:∠BOE=4:1,OE平分∠BOD

所以∠AOD:∠BOD=2:1,又因为∠AOD+∠BOD=180°,所以∠BOD=60°,∠AOD=120°

因为OF平分∠COB,所以∠COF=∠COB/2=∠AOD/2=60°,∠AOC=60°

所以∠AOF=∠AOC+∠COF=120°