# A polygon has 77 diagonals. Determine the number of sides ?

A polygon has 77 diagonals. Determine the number of sides ?

A. 15

B. 12

C. 17

D. 14

**Answer : **D. 14

## Explanation:

- The formula for the number of diagonals that can be formed in a polygon with n sides is.....

n(n - 3)/2 = D, where n = number of sides, D = total number of diagonals in the polygon.

n(n - 3)/2 = 77

n

^{2}- 3n = 154

n

^{2}- 3n - 154 = 0

n

^{2}- 14n - 11n - 154 = 0

n(n - 14) + 11(n - 14) = 0

(n - 14) (n + 11) = 0

**n = -11, 14**

Reject n=-11 and Accept n=14. Therefore, The number so sides of the **polygon is 14**.