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In a certain regular polygon, the measure of each interior angle is $2$ times the measure of each exterior angle. Find the number of sides in this regular polygon.

 Aug 7, 2024
 #1
avatar+37146 
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Interior angles of an   n-gon sum to   ( n-2) 180

exterior angles sum to 360 

so

(n-2)(180) / n  = 2 *  360 / n     solve for 'n'

180 - 360/n = 720 / n 

180 = 1080 / n 

180 n = 1080 

n = 6   sides 

 Aug 7, 2024

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