SOLUTION: determine the number of sides of a polygon whose exterior and interior angles are in the ratio 1 : 5

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Question 1040555: determine the number of sides of a polygon whose exterior and interior angles are in the ratio 1 : 5
Answer by ikleyn(52776) About Me  (Show Source):
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determine the number of sides of a polygon whose exterior and interior angles are in the ratio 1 : 5
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x for exterior angle and 5x for the interior angle.

x + 5x = 180  --->  6x = 180  --->  x = 180%2F6 = 30.

External angle is 30 degs.

n = 360%2F30 = 12.   (360° is the sum of the external angles of any n-sided polygon)

Answer.  n = 12.  ( Dodecagon !)