
Phan Thanh Tinh 20/04/2017 at 17:21
The measure of each interior angle of a regular ngon is :
\(\dfrac{180\left(n2\right)}{n}=\dfrac{180n360}{n}=180\dfrac{360}{n}\)
This measure is an integer when \(360⋮n\) and \(\dfrac{360}{n}< 180\)(n > 0)
=> n is a positive divisor of 360 and n > 2
360 = 2^{3} x 3^{2} x 5,so 360 has :
(3 + 1)(2 + 1)(1 + 1) = 24 (positive divisors)
Excluding n = 1 and n = 2,there are 22 values of n

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