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

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

Solution:

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 selecting 2 out of n = nC2

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

Number of diagonals of the polygon $={ }^{n} C_{2}-n=\frac{n(n-1)}{2}-n=\frac{n(n-3)}{2}$

 

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