n-sided regular polygon

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Can anyone help me on this? The method I used is to draw triangle, rectangular and so on, then try to find solution. But I feel it is not the best way and my answer seems wrong. Your help is deeply appreciated.

Problem: For how many values of n will an n-sided regular polygon have interior angles with integral degree measures?

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1 Answer

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An n-sided regular polygon's interior angle sum should be $180(n-2)$, so the interior angles would each be $\frac{{180^\circ \left( {n - 2} \right)}}{n}$. Then, these angles would have an integral value if either $180°$ or $n-2$ is divisible by $n$, or both are divisible by $n$. By counting these, you should get an answer.

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