MathDB

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}

3