如图所示,已知n边形A1A2A3A4A5.An,求证：∠A1+∠A2+∠A3+∠A4+∠A5+...∠An=(n-2)乘180°._数学解答

如图所示,已知n边形A1A2A3A4A5.An,求证：∠A1+∠A2+∠A3+∠A4+∠A5+...∠An=(n-2)乘180°.

人气：213 ℃　时间：2019-10-09 01:17:47

解答

证明：从n边形A1A2A3A4A5.An内部任选一点O,向所有顶点连线,分别是A1O,A2o,A3O,...,AnO一共n条线段这样得到△A1OA2,△A2OA3,△A30A4,...,△A(n-1)OAn,△AnOA1一共n个三角形,于是求得n边形A1A2A3A4A5.An内角和＝∠A1＋...