Question

已知∠AOB=80°，∠AOC=30°，則∠BOC=　　　　　　．                              

Answer 1

110°或50°　．                                                                                   

【考點】三角形內角和定理．                                                                  

【專題】分類討論．                                                                          

【分析】分兩種情況進行討論：①射線OC在∠AOB的外部；②射線OC在∠AOB的內部；從而算出∠AOC的度數．                                                                         

【解答】解：①射線OC在∠AOB的外部，如圖1，∠AOC=∠AOB+∠BOC=80°+30°=110°；                    

②射線OC在∠AOB的內部，如圖2，∠AOC=∠AOB﹣∠BOC=80°﹣30°=50°．                  

故答案為：110°或50°．                                                                          

                                         

【點評】本題考查了角的計算，在解答此題時要注意應用分類討論思想進行解答，不要漏解．