如圖，在同一平面內，將△ABC繞點A旋轉到△AED的位置，若AE⊥BC，∠ADC=65°，則∠ABC的度數為（...

問題詳情：

如圖，在同一平面內，將△ABC繞點A旋轉到△AED的位置，若AE⊥BC，∠ADC=65°，則∠ABC的度數為（　　）                                                                                     

A．30°                              B．40°                               C．50°                               D．60°

【回答】

B【考點】旋轉的*質．                                                                                     

【分析】先根據旋轉的*質得AD=AC，∠BAE=∠CAD，再根據等腰三角形的*質和三角形內角和計算出∠CAD=50°，則∠BAE=50°，然後利用互餘計算∠ABC的度數．                                                        

【解答】解：∵△ABC繞點A旋轉到△AED的位置，                                            

∴AD=AC，∠BAE=∠CAD，                                                                                 

∵AD=AC，                                                                                                        

∴∠ACD=∠ADC=65°，                                                                                     

∴∠CAD=180°﹣65°﹣65°=50°，                                                                           

∴∠BAE=50°，                                                                                                   

∵AE⊥BC，                                                                                                       

∴∠ABC=90°﹣∠BAE=40°．                                                                                 

知識點：圖形的旋轉

題型：選擇題