If a regular polygon has 20 diagonals, then the number of sides of this polygon is: 

Correct option is C

Given: 

Diagonals of a regular polygon  = 20

Concept Used:

For a polygon with $n$ sides, the formula to find the number of diagonals $D$ is

$$D = \frac{n(n-3)}{2}$$ 

solution:

the number of diagonals is 20.

Therefore:

​$$\frac{n(n-3)}{2} = 20$$ 

$$n^2 - 3n = 40$$

​$$n^2 - 3n - 40 = 0 \\ \ \\ n^2 - 8n +5n-40 = 0 \\ \ \\ n(n-8)+5(n-8) = 0 \\ \ \\ (n-8)(n+5) = 0$$  

n = 8 or n = -5 

​Since the number of sides$n$must be a positive integer, we discard$n=-5$and keep $n=8$.

Thus the polygon has 8 sides.