题目是用英文写的,Each exterior angle of a regular polygon of n sides

来源：学生作业帮编辑：拍题作业网作业帮分类：数学作业时间：2024/04/28 09:29:40

题目是用英文写的,
Each exterior angle of a regular polygon of n sides is 16 degree greater than each exterior angle of another regular polygon of 3n sides.
(a) Form an equation in n and solve for the value of n
(b) Calculate the interior angle of the regular polygon of 3n sides

正n边形的每个外角比正3n边形的每个外角大16°,（a）求n满足的方程并解出n（b）计算正3n边形的内角.

n多边形的外角和：360°,所以正n边形的每个外角：360°/n,正3n边形的每个外角：120°/n于是有
360°/n=120°/n+16°,也即：16n=240,解得n=15
正45边形的外角为：8°,所以内角为172°

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