Question

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

Answer 1

110°或50°　．                                                                                   

【考点】三角形内角和定理．                                                                  

【专题】分类讨论．                                                                          

【分析】分两种情况进行讨论：①射线OC在∠AOB的外部；②射线OC在∠AOB的内部；从而算出∠AOC的度数．                                                                         

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

②射线OC在∠AOB的内部，如图2，∠AOC=∠AOB﹣∠BOC=80°﹣30°=50°．                  

故答案为：110°或50°．                                                                          

                                         

【点评】本题考查了角的计算，在解答此题时要注意应用分类讨论思想进行解答，不要漏解．