I need to work out how many sides a regular polygon has when it's exterior angles are 20 degrees.

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For any regular polygon, the internal angle, A, of any n-sided polygon is given by A = 180 - 360/n.  Conversely, if we are given the internal angle, A, then the number of sides is gioven by  n = 360/(180-A).  If the exterior angle is 20° then the internal angle is 160°.  This means we have 18 sides in this polygon.
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