it is known that the sum of the interior angles of a regular polygon is at least 90度 greater than that of its exterior angles.Find the least possible number of sides of the polygon 书上answer是5.还有...要列出不等式啦...
问题描述：
it is known that the sum of the interior angles of a regular polygon is at least 90度 greater than that of its exterior angles.Find the least possible number of sides of the polygon
书上answer是5.
还有...要列出不等式啦...
答
x>=360+90=450
即x最小是540,所以是5边形
不等式中的360是因为任意多边形,外角和都是360度,90是题目说的
x是内角和
所以内角和大于等于外交和+90度
没有内角和会等于450,最小的是540
而540正是五边形的内角和
所以是五边形