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

Question

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

parthkohli · Answer

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.

anonymous · Answer

OH the same formula huh ok

parthkohli · Answer

Yep :P

anonymous · Answer

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