Question

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

（1）∠β的余角；                                                                             

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

Answer 1

                                                                                                          

【考点】余角和补角；度分秒的换算．                                                    

【分析】（1）根据互为余角的两个角的和为90度可得∠β的余角=90°﹣∠β，将∠β=41°31′代入计算即可；                

（2）将∠α=76°，∠β=41°31′代入2∠α﹣∠β，然后计算即可．                   

【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″．                                                                                    

【点评】此题考查了余角与补角，以及度分秒的换算，用到的知识点：                 

如果两个角的和等于90°（直角），就说这两个角互为余角．即其中一个角是另一个角的余角；              

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