Question

how many diagonals can be drawn with the help of n straight line figures?
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Answer 1

Answer:

A polygon of n sides has n vertices. By joining any two vertices of a polygon, we obtain either a side or a diagonal of the polygon. Number of line segments obtained by joining the vertices of a n sided polygon taken two at a time.

= Number of ways of selecting 2 out of n

=

n

C

2

=

2

n(n−1)

Out of these lines, n lines are the sides of the polygon.

∴ Number of diagonals of the polygon

=

2

n(n−1)

−n=

2

n(n−3)