CBSE Class 9 Answered

For a n sided figure,

 if you join each point to every other point you will have total number of line segments as [n(-1)]/2]

( we are dividing by 2 because line segments get repeated while counting. e.g. if we are counting a line segment from a point say A to another point C, then the same line segment gets counted when counting the number of line segments from C)

But this number contains all the sides and all the diagonals.

So the number of diagonals =

= total number of line segments - the number of sides

=[n(n-1)/2]-n

e.g

For a quadrilateral, n=4

so number of diagonals=[4(4-1)/2]-4

=6-4

=2

for a pentagon,

 the number of diagonals =

[5(5-1)/2]-5

=10-5

=5

you can verify this by drawing a figure.

This property can be generelised for n=100 and you will get the required answer.