SOLUTION: At each vertex of a regular n-gon, the ratio of the interior angle to the exterior angle is 5:1. Find the value of n

Question 1187046: At each vertex of a regular n-gon, the ratio of the interior angle to the exterior angle is 5:1. Find the value of n
Answer by ikleyn(52799) (Show Source): You can put this solution on YOUR website!
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At each vertex of a regular n-gon, the ratio of the interior angle to the exterior angle is 5:1.
Find the value of n
~~~~~~~~~~~~~~~~~~~~~~~~

Let x be the measure of the exterior angle;

then the measure of the interior angle is 5x, according to the condition.


Sp, we have


    x + 5x = 180  degrees,

     6x    = 180

      x    = 180/6 = 30.


Thus the exterior angle is 30 degrees, and the number of sides (= angles) of the regular n-gon is


      n =  = 12.     ANSWER

Solved.

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