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 because I have a test next Monday about interior and exterior angles and I don't understand how to find out how many sides it has. Can you please add a method of how you did it? Thanks soooo much! I really appreciate it :)

Guest Apr 25, 2015

#1**+10 **

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

Melody
Apr 25, 2015

#1**+10 **

Best Answer

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

Melody
Apr 25, 2015