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Two regular pentagons and a regular decagon, all with the same side length, can completely surround a point, as shown.

 

An equilateral triangle, another equilateral triangle, a square, and a regular n-gon, all with the same side length, also completely surround a point. Find n.

 

 Dec 29, 2023
 #1
avatar+126665 
+1

An interior angle of  the n-gon  will measure

 

360 - 2(60) - 90  = 150°

 

So

 

(n-2) / n * 180 =  150

 

180n - 360 = 150n

30n = 360

n = 360 / 30   =   12

 

 

cool cool cool

 Dec 29, 2023

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