What is the number of diagonals which can be drawn by joining the angular points of a polygon of $100$ sides?

4850

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4950

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5000

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10000

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Solution

The correct option is B $4850$
Diagonals can be formed by joining two opposite points.
Choosing 2 points from given points $=^{100} C_{2} = \frac{100 \cdot 99}{2} = 4950$
Total number of diagonals $=$ Number of lines joined by $2$ angular points of polygon $-$ Number of sides
$= 4950 - 100 = 4850$
Hence, option A is correct

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What is the number of diagonals which can be drawn by joining the angular points of a polygon of 100 sides?

The correct option is B 4850Diagonals can be formed by joining two opposite points.Choosing 2 points from given points =100C2=100⋅992=4950Total number of diagonals = Number of lines joined by 2 angular points of polygon − Number of sides=4950−100=4850Hence, option A is correct

What is the number of diagonals which can be drawn by joining the angular points of a polygon of $100$ sides?