How many diagonal lines are there in a 130-sided 
polygon?

The set of all pairs of vertices includes all the 
diagonals plus all of the 130 sides.  So to find 
the number of diagonals, we calculate the number 
of combinations of 130 vertices taken 2 at a time 
and then subtract the 130 sides.  So the answer is

C(130,2) - 130 =

130·129/2·1 - 130 =

8385 - 130 =

8255 diagonal lines

Edwin