Question

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

Answer 1

Answer:

hey mate,, here is your answer..

Step-by-step explanation:

We know that, to find diagonals of a polygon, we use the formula n(n-3)/2 where n is the number of sides. It is given that the polygon have 27 diagonals.

So,

=> n(n-3)/2=27

=> n²-3n=27×2

=> n²-3n=54

=> n²-3n-54=0

=> n²-(9–6)n-54=0

=> n²-9n+6n-54=0

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

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

n=-6 ; n=9

n should not be negative so 9 is the number of sides.

So the polygon have 9 sides which is also called a nanogon.

hope it helps u frnd !

Answer 2

answer is c 9 it has 9 sides