A polygon of n sides has n vertices. By joining any two vertices we obtain either a side or a diagonal.
∴ Number of ways of selecting 2 out of 9
Out of these lines, n lines are the sides of the polygon.
∴ Number of diagonals =
(i) In a hexagon, there are 6 sides.
∴ Number of diagonals =
(ii) There are 16 sides.
∴ Number of diagonals =