SOLUTION: At each vertex of a regular n-gon, the ratio of the interior angle to the exterior angle is 7:2. Find the value of n.

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Question 1208868: At each vertex of a regular n-gon, the ratio of the interior angle to the exterior angle is 7:2. Find the value of n.
Answer by ikleyn(52748) About Me  (Show Source):
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At each vertex of a regular n-gon, the ratio of the interior angle to the exterior angle
is 7:2. Find the value of n.
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Since the ratio of the interior angle to the exterior angle is 7:2,
we can write 7x for the interior angle measure, and 2x for exterior angle measure.


Then 7x + 2x = 180 degrees,  or  9x = 180 degrees, so  x = 180/9 = 20 degrees.


Thus the exterior angle is  2x = 2*20 = 40 degrees.


For exterior angle  alpha  of a regular polygon,  n%2Aalpha = 360  degrees.


It gives  n = 360/40 = 9.


ANSWER.  n = 9.

Solved.