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

          (1)∠β的余角;                                                                             

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


                                                                                                                    

          【考點(diǎn)】余角和補(bǔ)角;度分秒的換算.                                                    

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

          (2)將∠α=76°,∠β=41°31′代入2∠α﹣∠β,然后計(jì)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(diǎn)評(píng)】此題考查了余角與補(bǔ)角,以及度分秒的換算,用到的知識(shí)點(diǎn):                 

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

                                                                                                                 


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