Diagonals of polygons

How many diagonals does an n-gon have? n(n−3)/2.

Diagonals are line segments connecting non-adjacent vertices.

Build a polygon

regular heptagon

interior each
128.6°

exterior each
51.4°

interior sum
900°

diagonals
14

Number of diagonals

n (n - 3) /2

Try it

Hexagon (n=6)

6·3/2 = 9 diagonals.