which polygon out of a regular nonagon, decagon and undecagon has 35 diagonals?

Question

geez someone help me. i've been trying to figure this out for way too long.

Answer 1

It would be the decagon..this is a pattern problem

A triangle has 0 diagonals
A quad has 2
A pentagon has 5
A hexagon has 9

You see the numbers go up by 2, then 3, then 4......so by the time you get to decagon, you'll have 35.

There is a formula for this also but sometimes I forget what it is but I can always draw a couple figures to see the pattern again

Answer 2

10 (decagon)

Number of diagonals =
(number of sides - 3) * (number of sides) / 2