+0  
 
0
46
4
avatar

In a certain regular polygon, the measure of each interior angle is 12 times the measure of each exterior angle. Find the number of sides in this regular polygon.
 

 May 10, 2020
 #1
avatar
0

 

If I knew the value of an angle I could work backwards from (n – 2) • 180. 

 

To obtain the value of an angle, I'm going to have to divide 180 by 13. 

 

That division doesn't come out even, so I'm stuck there.  Sorry. 

 May 10, 2020
 #2
avatar
0

The answer is 36 sides.

 May 12, 2020
 #3
avatar
0

 

Let's try it out. 

 

Using (n – 2) x 180o we find the sum of all 36 angles  =   6,120o 

 

Since it's a regular polygon each of the 36 angles must equal 6,120o / 30  =   170o 

 

This leaves only 10o for the external angle.  That doesn't have the required 12 to 1 ratio. 

 

Have I made a mistake somewhere?  What say you? 

.

Guest May 12, 2020
 #4
avatar
0

 

Jeeze, I swear I proofread it a dozen times before publishing.  And yet, this.... 

 

The line should be 

 

Since it's a regular polygon each of the 36 angles must equal 6,120o / 36  =  170o 

.

Guest May 12, 2020

16 Online Users