凸多边形的边数与顶点数、内角和、外角和、对角线条数都有着相依的关系,分析这些关系, 便可确定边数,下面列举十例予以说明．例1 如果一个多边形的边数增加1倍,它的内角和是2160°,求原来多边形的边数．分析设原来多边形的边数为n,那么边数增加1倍后的多边形边数为2n,内角和为 (2n-2)×180°,由题意得 The number of edges and the number of vertices, internal angles, external angles, and diagonal lines of a convex polygon are all dependent on each other. By analyzing these relationships, the number of edges can be determined. The following ten examples are given. Example 1 If the number of sides of a polygon is increased by 1 and its inner angle is 2160°, find the number of sides of the original polygon. The analysis assumes that the number of edges of the original polygon is n, then the number of edges of the polygon after the number of edges increases by 1 is 2n, and the internal angle is (2n-2)×180°.