If each interior angle of a regular polygon is $156^{\circ}$, the number of sides is:

If each interior angle of a regular polygon is $156^{\circ}$, the number of sides is:
  1. $12$
  2. $15$
  3. $18$
  4. $20$

Solution

Each exterior angle $= 180 - 156 = 24^{\circ}$. So $n = \dfrac{360}{24} = 15$.

Asked in: IMO

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