+0  
 
0
115
2
avatar

An equiangular polygon with n sides has \(162\)-degree interior angles. Find the integer n.

 Feb 18, 2022
 #1
avatar+36434 
+1

The EXterior angles will be    180 - 162 = 18 degrees

     EXterior angles sum to 360

        360 / 18 = n

 Feb 18, 2022
 #2
avatar+2444 
0

You could also write it as an equation:

 

\(n\) = number of sides in the polygon

 

\(162n=180(n-2)\)

\(162n=180n-360\)

\(0=18n-360\)

\(18n=360\)

\(n = 20\)

 

So, the polygon has \(\color{brown}\boxed{20}\) sides like Pavlov said.

 

(His method is the better method tho...)

 Feb 18, 2022

16 Online Users