Question

如圖，已知OD平分∠AOB，射線OC在∠AOD內(nèi)，∠BOC=2∠AOC，∠AOB=114°．求∠COD的度數(shù)．               

                                                                             

Answer 1

【考點】角的計算；角平分線的定義．                                                    

【專題】探究型．                                                                              

【分析】根據(jù)OD平分∠AOB，射線OC在∠AOD內(nèi)，∠BOC=2∠AOC，∠AOB=114°，可以求得∠AOC、∠AOD的度數(shù)，從而可以求得∠COD的度數(shù)．                                                                 

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

∴∠AOD=∠BOD==57°．                                                           

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

∴∠AOC=．                                                                     

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

【點評】本題考查角的計算，解題的關鍵是找出所求問題需要的條件．