1981 USAMO Problems/Problem 4

Problem

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 $n=3$ .

Solution

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1981 USAMO (Problems • Resources)
Preceded by Problem 3	Followed by Problem 5
1 • 2 • 3 • 4 • 5
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1981 USAMO Problems/Problem 4

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