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A Common Vertex (Posted on 2004-07-12) Difficulty: 2 of 5
Three regular polygons, all with unit sides, share a common vertex and are all coplanar. Each polygon has a different number of sides, and each polygon shares a side with the other two; there are no gaps or overlaps. Find the number of sides for each polygon. There are multiple answers.

See The Solution Submitted by Brian Smith    
Rating: 3.0000 (1 votes)

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a few | Comment 8 of 19 |
to meet the requirements, the sum of the inside angles of
the polygons should be 180 degrees. i've found four com-
binations that i believe will work.

-square: 90 (degrees of inner angle)
-hexagon: 120
-12 sided: 150 (is that called a dodecagon?)

-triangle: 60
-9 sided: 140
-18 sided: 160

-triangle: 60
-octagon: 135
-24 sided: 165

-square: 90
-pentagon: 108
-20 sided: 162

there are more combinations. i'll post if i find any.








  Posted by rixar on 2004-07-12 19:26:03
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