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How many polygons have interior angles of integral measure? 

 Dec 25, 2018

Best Answer 

 #1
avatar+192 
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We first go by the exterior angle measure: \(\frac{360}{n}\).

 

Now, \(n\) has to be a factor of \(360\) , so we count how many factors this number has.

 

Since \(360=2^3*3^2*5\)\(\) , we add one to each power, resulting in    \(4*3*2=24\) factors.

 

Finally, a polygon cannot have one or two sides; thus the answer is \(24-2=\boxed{22}\) regular polygons.

 Dec 25, 2018
 #1
avatar+192 
+2
Best Answer

We first go by the exterior angle measure: \(\frac{360}{n}\).

 

Now, \(n\) has to be a factor of \(360\) , so we count how many factors this number has.

 

Since \(360=2^3*3^2*5\)\(\) , we add one to each power, resulting in    \(4*3*2=24\) factors.

 

Finally, a polygon cannot have one or two sides; thus the answer is \(24-2=\boxed{22}\) regular polygons.

azsun Dec 25, 2018

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