help f2 maths !!!

👨🏻‍🏫 學術台數學

[匿名]

2013-11-20 1:36 am

If the size of each exterior angle of a regular n-sided is x, where x is an integer, find two possible values of n such that n is greater than 20.

Step+ans please
thanks

更新1:

I know that the ans is 24 30 36 40 45 60 72 90 120 180 or 360 but I don't know how to do please give me the step thanks a lot

回答 (1)

用戶4366

2013-11-20 2:05 am

✔ 最佳答案

All the Exterior Angles of a polygon add up to 360°, so:

Each exterior angle must be 360°/n

x = 360/n

x has to be an integer.

360 = 2x2x3x3x2x5 = (2^3)(3^2)(5)

factors of 360 = 2 , 3, 4, 5, 8, 9 ........

n = 2x2x2x3 = 24
or
n = 2x2x2x5 = 30
or
....
....

2013-11-19 18:54:11 補充：
factors of 360 = 2 , 3, 4, 5, 6, 8, 9 ........

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