Write the number of diagonals of an n-sided polygon.

1.	Write the number of diagonals of an n-sided polygon.
Answer» An n-sided polygon has n vertices. By joining any two vertices of the polygon, we obtain either a side or a diagonal of the polygon. Number of line segments obtained by joining the vertices of an n-sided polygon if we take two vertices at a time, number of Ways of selection 2 out of n = ⁿC₂ Out of these lines, n lines are sides of the polygon. Number of diagonals of the polygon = ⁿC₂ – n = \(\frac{n(n-1)}{2}\) - n = \(\frac{n(n-3)}{2}\)

Answer»

An n-sided polygon has n vertices.

By joining any two vertices of the polygon, we obtain either a side or a diagonal of the polygon.

Number of line segments obtained by joining the vertices of an n-sided polygon if we take two vertices at a time, number of

Ways of selection 2 out of n = ⁿC₂

Out of these lines, n lines are sides of the polygon. Number of diagonals of the polygon =

ⁿC₂ – n = \(\frac{n(n-1)}{2}\) - n

= \(\frac{n(n-3)}{2}\)

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