Question

A polygon has 35 diagonals. How many sides does it have?

Answer 1

The diagonals of a ploygon with "n" sides can be found out using the formula :
  (n²-3n)/2
So according to the formula: (n²-3n)/2=35
                                               ⇒(n²-3n)=70
                                               ⇒n²-3n-70=0
                                               ⇒(n-10)(n+7)=0
As n cannot be negative 
the number of sides of the polygon=10
                                              

Answer 2

Answer:

n(n-3)/2=35

n(n-3)=35*2=70

Step-by-step explanation:

(n)2-3n-70=0

n=10