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
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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(52795) (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 5:1.
Find the value of n
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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
