Question

已知∠α=76°，∠β=41°31′，求：                                                             

（1）∠β的余角；                                                                             

（2）∠α的2倍與∠β的的差．                                                            

Answer 1

                                                                                                          

【考點】余角和補角；度分秒的換算．                                                    

【分析】（1）根據互為余角的兩個角的和為90度可得∠β的余角=90°﹣∠β，將∠β=41°31′代入計算即可；                

（2）將∠α=76°，∠β=41°31′代入2∠α﹣∠β，然后計算即可．                   

【解答】解：（1）∠β的余角=90°﹣∠β                                                 

=90°﹣41°31′                                                                                      

=48°29′；                                                                                           

（2）∵∠α=76°，∠β=41°31′，                                                               

∴2∠α﹣∠β=2×76°﹣×41°31′                                                             

=152°﹣20°45′30″                                                                               

=131°14′30″．                                                                                    

【點評】此題考查了余角與補角，以及度分秒的換算，用到的知識點：                 

如果兩個角的和等于90°（直角），就說這兩個角互為余角．即其中一個角是另一個角的余角；              

度、分、秒是常用的角的度量單位．1度=60分，即1°=60′，1分=60秒，即1′=60″．