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# polygon

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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

### 2+0 Answers

#1
+2437
+1

Write as equation:

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

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

Mar 11, 2022
#2
+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