Problem
COM-B1-M04-P011 Endpoints of Diagonals
#11
★★☆☆☆ Level 2 of 5
Derive the formula for the number of diagonals of an \(n\)-gon by counting diagonal endpoints.
From each vertex, \(n-3\) diagonals are drawn.
From each of the \(n\) vertices, \(n-3\) diagonals are drawn, so there are \(n(n-3)\) diagonal endpoints. Each diagonal has two endpoints, so the number of diagonals is \(n(n-3)/2\).
Same principle as the sum of degrees.