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The interior angles of a convex polygon are in arithmetic progression. The smallest angle is 120 degrees and the common difference is 5 degrees. Find the number of sides of the polygon.

 Mar 11, 2022
 #1
avatar+2437 
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Write as equation:

\(180(s-2) = s({120 + (120+5s) \over 2})\)

 

By solving, \(\color{brown}\boxed{s = 12}\)

 Mar 11, 2022
 #2
avatar+2437 
+1

***EDIT*** 

 

I forgot to write the arithmetic series part correctly. The equation should be: 

 

\(180(s-2) = s{(120 + (120 + 5(s-1)) \over 2}\)

 

Solving, we find it can be 9, or 16. It can't be 16, because the largest angle is greater than 180, and then it would not be a convex polygon. 

 

Thus, the CORRECT answer is \(\color{brown}\boxed{9}\)

 

Thank You Geno for telling me!!!

BuilderBoi  Mar 11, 2022

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