已知一个正多边形的每个内角都比它的外角的4倍还多90°,求这个正多边形的边数及内角和
人气:119 ℃ 时间:2020-04-23 08:55:19
解答
∵正n边形的每个内角都比它的外角的4倍还多90°,
设正多边形一内角为X,一外角为Y
∴X=4×Y+90º 内角和=﹙n-2﹚×180º
Y=360º/n
∴﹙n-2﹚×180º=n×﹙4×360º/n+90º﹚
∴n=20
∴这个正多边形的边数n=20
内角和﹙20-2﹚×180=3240º
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