Question

如圖，AB∥CD，CB平分∠ABD．若∠C=40°，則∠D的度數(shù)為（　　）               

                                                                                  

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

Answer 1

B

【考點(diǎn)】平行線的性質(zhì)．                                                                         

【分析】先利用平行線的性質(zhì)易得∠ABC=40°，因?yàn)镃B平分∠ABD，所以∠ABD=80°，再利用平行線的性質(zhì)兩直線平行，同旁內(nèi)角互補(bǔ)，得出結(jié)論．                                                                     

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

∴∠ABC=40°，                                                                                  

∵CB平分∠ABD，                                                                            

∴∠ABD=80°，                                                                                 

∴∠D=100°．                                                                                    

故選B．                                                                                            

【點(diǎn)評】本題主要考查了平行線的性質(zhì)和角平分線的定義，利用兩直線平行，內(nèi)錯(cuò)角相等；兩直線平行，同旁內(nèi)角互補(bǔ)是解答此題的關(guān)鍵．