How can I do this exercise: the size of each exterior angle of a regular polygon is 20 degrees. Work out how many sides the polygon has. Thank you! It's

If the exterior angle is 20 degrees then the interior angle must be 160 degrees

The sum of the interior angles of a polygon with n sides = (n-2)*180

Each individual internal angle in a regular polygon ((n-2)*180)/n

$$\\\frac{(n-2)*180}{ n}=160\\ (n-2)*180=160n\\ 180n-360=160n\\ 20n=360\\ n=18$$

18 sides

Note that Melody's answer can be generalized as:

The measure of the exterior angle =

180 - [(n - 2)*180 / n]  =

[180n - 180n + 360] / n =

360/n   where n is the number of sides

Then.....  

360/n  = 20

20n = 360

n = 18