+0  
 
0
48
8
avatar

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

 Jul 18, 2021
 #1
avatar+27 
+1

n = 20

 Jul 18, 2021
 #2
avatar
0

ok...but how you get that?

Guest Jul 18, 2021
 #3
avatar+63 
+1

In order to complete a 360 degree rotation on the outer sides, we simply find the rotation by subtracting 162 from 180, finding the vertical outer angle

 

180-162=18

 

18! Great! Now, it takes 360 degrees to complete one full circular rotation, so we take 360 and divide it by 18, which gives us 20, which is the amount of sides, if each side has an exterior vertical angle of 18. We have one angle that connects 2 sides, so 

 

 The answer is \(20 sides\)

 Jul 18, 2021
edited by PBJcatalinasandwich  Jul 18, 2021
 #4
avatar
0

just google searched it, an angle of it is 162 and 1/9

Guest Jul 18, 2021
 #5
avatar
+1

The answer is an icosagon i think, which has 20 sides

Guest Jul 18, 2021
 #6
avatar+63 
0

Well, glad you found it! laugh

PBJcatalinasandwich  Jul 18, 2021
 #7
avatar+63 
0

Ah. Forgive clumsy me. I thought that there was an extra angle :P

PBJcatalinasandwich  Jul 18, 2021
 #8
avatar+86 
+3

For future reference, the measure of the angles in an equaingular polygon with n sides is \((n-2)\cdot180\over n\).

 Jul 19, 2021

12 Online Users