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