Question

A polygon has 27 diagonals. How many sides does it have?

(a) 7 (b) 8 (c) 9 (d) 12

Answer 1

(c) 9

Explanation:

We know that to calculate number of diagonals in octagon is

Number of diagonals is= n × (n -3)/2

27= n × (n -3)/2

n (n-3) = 54

n²– 3n = 54

n²– 3n-54 = 0

(n + 6) (n – 9)=0

n=-6 or n=9

So that we are calculating the sides it should be positive, therefore sides of polygon has 27 diagonals is 9