SOLUTION: Show that no regular polygon can have vertex angles which are 110

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Question 621044: Show that no regular polygon can have vertex angles which are 110
Answer by fcabanski(1391) About Me  (Show Source):
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The formula for the sum of the interior angles (vertices) of a polygon is (n-2)180 where n is the number of sides, and must be a whole number. A polygon has 3 or 4 or 5 or... some whole number of sides.


A regular polygon has each vertex measure the sum of the interior angles ( (n-2)180) divided equally amongst the number of sides n: %28n-2%29180+%2F+n.


Can this equal 110 when n is a whole number?


%28n-2%29180+%2F+n+=+110 | multiply both sides by n and distribute the 180


180n - 360 = 110n | Add 360 to both sides and subtract 110 n from both sides.


70n = 360 so n = 360/70 = 36/7 - which isn't a whole number. This polygon would have to have 5 and 1/7 sides. That's not possible.

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