The exterior angle of a regular polygon equals one-third of its interior angle. The polygon has:

The exterior angle of a regular polygon equals one-third of its interior angle. The polygon has:
  1. $6$ sides
  2. $8$ sides
  3. $10$ sides
  4. $12$ sides

Solution

Let exterior $= x$, interior $= 3x$. Then $x + 3x = 180 \Rightarrow x = 45^{\circ}$. So $n = \dfrac{360}{45} = 8$.

Asked in: IMO

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