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If the number of diagonals of a 'n' sided polygon is 560, then find the value of n.
1. 35
2. 32
3. 36
4. 37

1 Answer

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Correct Answer - Option 1 : 35

Given:

The number of diagonals of a 'n' sided polygon is 560

Formula used:

Number of diagonal in the polygon = a(a – 3)/2 

Where,

a → Number of sides in the polygon

Calculation:

n(n - 3)/2 = 560

⇒ n2 - 3n - 1120 = 0

⇒ n2 - 35n + 32n - 1120 = 0

⇒ n(n - 35) + 32(n - 35) = 0

⇒ (n + 32) (n - 35) = 0

⇒ n = - 32 and 35

But n can't be - 32 as it's negative.

So, n = 35

∴ value of n is 35

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