An interior angle of a regular polygon is $5$ times its exterior angle. The number of sides is:

An interior angle of a regular polygon is $5$ times its exterior angle. The number of sides is:
  1. $10$
  2. $12$
  3. $15$
  4. $18$

Solution

Let exterior angle be $x$. Interior $= 5x$. Then $x + 5x = 180 \Rightarrow 6x = 180 \Rightarrow x = 30^{\circ}$. So $n = \dfrac{360}{30} = 12$.

Asked in: IMO

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