The exterior angle of a regular polygon cannot be:

The exterior angle of a regular polygon cannot be:
  1. $60^{\circ}$
  2. $45^{\circ}$
  3. $22^{\circ}$
  4. $24^{\circ}$

Solution

$\dfrac{360}{22}$ is not an integer (it equals $\approx 16.36$), so $22^{\circ}$ cannot be the exterior angle of a regular polygon. The other values ($60, 45, 24$) all divide $360$ evenly.

Asked in: IMO

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