The exterior angle is the supplement of the interior angle. We know the sum of the interior angles is (N-2)*180 degrees for an N-sided polygon. Summing the interior angles, we get to the same conclusion Dragonfire came to: The sum of the exterior angles is always 360 degrees. Let N = the number of sides in your regular polygon.

Summing interior angles, we have ...

N(180-12) = (N-2)180 = 180N-360

360 = N(180 - (180-12)) = 12N

360/12 = 30 = N

Summing interior angles, we have ...

N(180-12) = (N-2)180 = 180N-360

360 = N(180 - (180-12)) = 12N

360/12 = 30 = N