Question

5. A polygon has 27 diagonals. How many sides does it have?
(a) 7
(b) 8
(6) 9
(d) 12
​

Answer 1

Answer:

c) 9

Step-by-step explanation:

hope it helps you.

Answer 2

Answer:

9

Step-by-step explanation:

We know that,

Number of diagonals of a polygon =   $\frac{n(n-3)}{2}$

Its given that

$\frac{n(n-3)}{2}$  = 27

n(n - 3) = 54  

$n^{2} - 3n - 54 = 0$

$n^{2}$ - 9n + 6n - 54 = 0

n(n-9) + 6(n-9) = 0

(n-9)(n+6) = 0

n = 9, - 6 (Neglecting negative value)

n = 9  

Hence, sides of polygon are 9.