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Naming the Polygon

Find the numb...

Question

Find the number of diagonals of a polygon of 10 sides.

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Solution

Assume that there are 10 points in a plane where no 3 of them are collinear which are the vertices of the given polygon.
The number of different lines that can be formed by joining these 10 points is ${10_{C}}_{2}$ .
Hence, the required number of diagonals = Number of lines formed - Number of sides of the polygon
$= {10_{C}}_{2} - 10 = 35$

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