如图,AB∥CD,∠BED=110°,BF平分∠ABE,DF平分∠CDE,则∠BFD=(  ) A.110° B.115° C.125° D.130°

问题描述:

如图,AB∥CD,∠BED=110°,BF平分∠ABE,DF平分∠CDE,则∠BFD=(  )
A. 110°
B. 115°
C. 125°
D. 130°

过点E作EM∥AB,过点F作FN∥AB,

∵AB∥CD,
∴EM∥AB∥CD∥FN,
∴∠ABE+∠BEM=180°,∠CDE+∠DEM=180°,
∴∠ABE+∠BED+∠CDE=360°,
∵∠BED=110°,
∴∠ABE+∠CDE=250°,
∵BF平分∠ABE,DF平分∠CDE,
∴∠ABF=

1
2
∠ABE,∠CDF=
1
2
∠CDE,
∴∠ABF+∠CDF=
1
2
(∠ABE+∠CDE)=125°,
∵∠DFN=∠CDF,∠BFN=∠ABF,
∴∠BFD=∠BFN+∠DFN=∠ABF+∠CDF=125°.
故选C.