Question

初二数学题，求解！

已知△ABC中，∠ABC=80°，CE是∠ACB的外角平分线，CE的反向延长线与∠BAC的平分线相交于点F，求∠F的大小

Answer 1

如图所示，根据三角形的性质来解决

Answer 2

∠F=∠ABC+∠BAF-∠BCF=∠ABC+1/2∠BAC-∠DCE=∠ABC+1/2∠BAC-1/2∠DCA
=∠ABC-1/2(∠DCA-∠BAC)=∠ABC-1/2∠ABC=1/2∠ABC=40°