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

A square, a regular pentagon, and a regular n-gon, all with the same side length, also completely surround a point. Find n.

 

Please let me know how you achieved your answer! A small hint would be extremely appreciated! Thank you so much! 

 Jul 25, 2020
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When you put a regular pentagon and a square next to each other, their sides create an angle of 162º. 

 

The internal angle of a pentagon is 108º  and of a square 90º.        360º - ( 108º + 90º ) = 162º

 

I'll let you find that n-gon.  laugh

 Jul 25, 2020

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