In a quadrilateral, a student can draw two diagonals. In a pentagon, a student can draw five diagonals. In a hexagon, a student can draw nine different diagonals. How many diagonals can be drawn in a regular polygon that has 17 sides?

Hello,

Let's assume a polygonal of n vertices.

Starting from of vertice we can reach n-1 vertices by 2 must be excluded.

So there are n * (n-1-2) possibilities but each possibility is counted twice

Number of diagonals = n (n-3) / 2

Examples:

n=4==>#=4 * (4-3) / 2=4*1/2=2

n=5==>#=5 (5-3) / 2=5*2/2=5

n=6==>#=6 * (6-3) / 2=6*3/2=9

n=17==>#=17 * (17-3) / 2=119.