The number of diagonals in a polygon of n sides is:

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The number of diagonals in a polygon of n sides is:

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n n − 2 2

n n − 3 2

n n − 4 2

n n − 5 2

answer is B.

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Detailed Solution

We need to find the number of diagonals in a polygon of n sides.
Number of diagonals of polygons having n sides

= n n − 1 2 − n

.
Simplifying,

⇒ n n − 1 2 − n 1

⇒ n n − 1 2 − 2 × n 1 × 2

⇒ n n − 1 2 − 2 n 2

⇒ n n − 1 − 2 n 2

⇒ n n − 1 − 2 2 ⇒ n n − 3 2

Therefore, the number of diagonals in a polygon of side n is

n n − 3 2

.
Hence, option 2 is correct.

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