Question

如图，已知OD平分∠AOB，射线OC在∠AOD内，∠BOC=2∠AOC，∠AOB=114°．求∠COD的度数．               

                                                                             

Answer 1

【考点】角的计算；角平分线的定义．                                                    

【专题】探究型．                                                                              

【分析】根据OD平分∠AOB，射线OC在∠AOD内，∠BOC=2∠AOC，∠AOB=114°，可以求得∠AOC、∠AOD的度数，从而可以求得∠COD的度数．                                                                 

【解答】解：∵OD平分∠AOB，∠AOB=114°，                                             

∴∠AOD=∠BOD==57°．                                                           

∵∠BOC=2∠AOC，∠AOB=114°，                                                         

∴∠AOC=．                                                                     

∴∠COD=∠AOD﹣∠AOC=57°﹣38°=19°．                                            

【点评】本题考查角的计算，解题的关键是找出所求问题需要的条件．