CMO 1995 Problem 3

Define a boomerang as a quadrilateral whose opposite sides do not intersect and one of whose internal angles is greater than $180^{\circ}$ . Let $C$ be a convex polygon with $s$ sides. The interior region of $C$ is the union of $q$ quadrilaterals, none of whose interiors overlap each other. $b$ of these quadrilaterals are boomerangs. Show that $q\ge b+\frac{s-2}{2}$ .