Question

If a polygon has 35 diagonals,find the number of sides in the polygon? Select one: a. 25 b. Cant be determined. C. 10 d. 30

Answer 1

No. of diagonal = n ( n-3)/2 = 35

⇒ n² - 3 n - 70 = 0

⇒ n² - 10 n + 7 n - 70 = 0

⇒ n ( n-10) + 7 ( n - 10) = 0

⇒ ( n + 7 )( n - 10)=0

∴ n = -7 or 10

-7 can't possible .

That's why n = 10