题目

已知∠α=76°，∠β=41°31′，求：                                                              （1）∠β的余角；                                                                              （2）∠α的2倍与∠β的的差．                                                             答案：                                                                                                           【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″．                  　                                                                                                      

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