The number of diagonals to a regular polygon A is given as 20. What is the exterior angle of the regular polygon A?

The number of diagonals formula is given as $$\dfrac{n\left(n\ -\ 3\right)}{2}$$. The number of diagonals is given as 20 in the questions. The number of sides can be calculated as.

$$\dfrac{n\left(n\ -\ 3\right)}{2}\ =\ 20$$

$$n\left(n\ -\ 3\right)\ =\ 40$$

$$n^2\ -3n\ -\ 40\ =\ 0$$

$$n^2\ -\ 8n+\ 5n\ -\ 40\ =\ 0$$

$$\left(n\ +\ 5\right)\left(n\ -\ 8\right)\ =\ 0$$

$$n\ =\ 8\ or\ n\ =\ -5$$

Since n cannot be negative, the value of n is 8.

The exterior angle can be calculated as $$\dfrac{360}{n}\ =\ \dfrac{360}{8}\ =\ 45^{\circ\ }$$

The correct answer is option B.