1981 USAMO Problems/Problem 4


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 $n=3$.


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See Also

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

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