Question

如图，AB∥CD，CB平分∠ABD．若∠C=40°，则∠D的度数为（　　）               

                                                                                  

A．90°                         B．100°                       C．110°                       D．120°

Answer 1

B

【考点】平行线的性质．                                                                         

【分析】先利用平行线的性质易得∠ABC=40°，因为CB平分∠ABD，所以∠ABD=80°，再利用平行线的性质两直线平行，同旁内角互补，得出结论．                                                                     

【解答】解：∵AB∥CD，∠C=40°，                                                      

∴∠ABC=40°，                                                                                  

∵CB平分∠ABD，                                                                            

∴∠ABD=80°，                                                                                 

∴∠D=100°．                                                                                    

故选B．                                                                                            

【点评】本题主要考查了平行线的性质和角平分线的定义，利用两直线平行，内错角相等；两直线平行，同旁内角互补是解答此题的关键．