Complete the analogy, in which each number counts the diagonals of the shape named: Quadrilateral : 2 :: Pentagon : ?

From each of the 5 corners of a pentagon a diagonal runs to the 2 corners that are not next to it, giving $5\times 2=10$ ends; every diagonal has been counted at both of its ends, so there are 5 diagonals. The same count on a quadrilateral gives $4\times 1÷2=2$, which agrees with the pair given. The trap 10 is that count left unhalved. 4 comes from reading the rule as one less than the number of sides, which fails the given pair because 4 − 1 = 3, not 2. 3 is the number of triangles a pentagon splits into when one corner is joined to all the rest.