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