Question

A polygon has 434 diagonals. number of sides=

Answer 1

we know the formula ,
   number of diagonals = n(n - 3)/2 ,where n is the number of sides .
here given,
  number of diagonals = 434 
  ⇒ n(n - 3)/2 = 434 
⇒ n² - 3n = 868 
⇒ n² - 3n - 868 = 0 
⇒ n² - 31n + 28n - 868 = 0
⇒ n( n - 31) + 28(n - 31) = 0
⇒ (n - 31)(n + 28) = 0
n = 31 and - 28 ,  n ≠ - 28 , number o sides can't be negative.
  hence, number of sides = 31

Answer 2

the number of sides are 217.