The ratio of interior angle to exterior angle of a regular polygon is $7:2$. Number of sides is:

The ratio of interior angle to exterior angle of a regular polygon is $7:2$. Number of sides is:
  1. $7$
  2. $8$
  3. $9$
  4. $10$

Solution

Let interior $= 7k$, exterior $= 2k$. Then $7k + 2k = 180 \Rightarrow k = 20$. Exterior $= 40^{\circ}$. So $n = \dfrac{360}{40} = 9$.

Asked in: IMO

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