The exterior angle of a regular polygon is $40$ degrees, how many sides does it have?

Question

I have used the formulae $(n-2) \times 180^{\circ}$ and I have tried to work in algebra but I just can't do it

Answer 1

That is not the fastest solution, but your $(n-2)\times 180^\circ$ is the sum of the interior angles.

Since the polygon is regular, each interior angle is therefore $\dfrac{n-2}{n}\times 180^\circ$. This should be equal to $180^\circ - 40^\circ$ so you can write an equation and solve for $n$.

Answer 2

Exterior angles (in a regular polygon) add to 360°. So you would do $360/40$ to get an answer of 9.