More Tricks With Triangulations

Please comment your solutions, questions and remarks..

I learned this riddle from Sergei Chmutov. It is also a problem concerning triangulation and sharp angled triangles. Suppose we have a triangulated regular polygon with odd number of edges. The vertices of the triangles must coincide with the vertices of the polygon like in the picture below. Show that exactly one triangle has only acute (sharp) angles and all other triangles have at least one obtuse (blunt) angle.

Triangulated heptagon


About Vadim Kulikov

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