OpenStudy (anonymous):

The exterior angle measure of a regular polygon is 20 degrees. How many sides does the polygon have? 9 16 18 20

6 years ago
Parth (parthkohli):

Interior angle would be 180 - 20 = 160 Now that we know this, let's use the formula. $$\Large \color{MidnightBlue}{\Rightarrow {180n - 360 \over n} = 160 }$$ $$\Large \color{MidnightBlue}{\Rightarrow 160n = 180n - 360 }$$ $$\Large \color{MidnightBlue}{\Rightarrow 0 = 20n - 360 }$$ $$\Large \color{MidnightBlue}{\Rightarrow -20n = -360 }$$ $$\Large \color{MidnightBlue}{\Rightarrow 20n = 360 }$$ $$\Large \color{MidnightBlue}{\Rightarrow n = 18 }$$ 18 sides.

6 years ago
OpenStudy (anonymous):

OH the same formula huh ok

6 years ago
Parth (parthkohli):

Yep :P

6 years ago
OpenStudy (anonymous):

(2n-4)*9=16n => 18n-36=16n => 2n=36=> n=18

6 years ago