USAMO 1981 Problem 4

A convex polygon has $\mathrm{n}$ sides. Each vertex is joined to a point $\mathrm{P}$ not in the same plane. If $\mathrm{A}, \mathrm{B}, \mathrm{C}$ are adjacent vertices of the polygon take the angle between the planes PBA and PBC. The sum of the $n$ such angles equals the sum of the $\mathrm{n}$ angles subtended at $\mathrm{P}$ by the sides of the polygon (such as the angle APB). Show that $\mathrm{n}=3$.