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Question
Find the number of diagonals of an n-sided polygon. In particular, find the number of diagonals when n = 10
Solution
In an n-sided polygon, there are ‘n’ points and ‘n’ sides.
∴ Through ‘n’ points we can draw nC2 lines including sides.
∴ Number of diagonals in n sided polygon
= nC2 – n .........(n = number of sides)
n = 10
nC2 – n = 10C2 – 10
= `(10 xx 9)/(1 xx 2) - 10`
= 45 – 10
= 35
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