Question

how many diagonals does a hexagon, heptagon, octagon, and do-decagon have?

Answer 1

Example, a hexagon has 6 vertices with 3 diagonals coming from each, so
6 x 3=18, 18/2= 9, the hexagon should have 9 diagonals possible. It is not 18 because you cannot count the same diagonal twice.

With further exploration, I created the following formula:
\[diagonal = n(n-3)/2\]