1981 USAMO Problems/Problem 4

Revision as of 19:12, 3 July 2013 by Etude (talk | contribs)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)


A convex polygon has $n$ sides. Each vertex is joined to a point $P$ not in the same plane. If $A, B, C$ are adjacent vertices of the polygon take the angle between the planes $PAB$ and $PBC$. The sum of the $n$ such angles equals the sum of the $n$ angles in the polygon. Show that $n=3$.


This problem needs a solution. If you have a solution for it, please help us out by adding it.

See Also

1981 USAMO (ProblemsResources)
Preceded by
Problem 3
Followed by
Problem 5
1 2 3 4 5
All USAMO Problems and Solutions

The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. AMC logo.png

Invalid username
Login to AoPS