A convex polygon has its interior angles in arithmetic progression, the least angle being $120°$ and common difference $5°$. Find the number of sides of the polygon.

To solve this I use the fact that the sum of the interior angles of a convex polygon in $(n-2)180°$. We can write the equation

$$120n + \frac{n(n-1)}{2}5 = (n-2)180.$$

Solving this we get the polynomial $n^2-25n+144=0$. This admits two solutions $9 \ \& \ 16$.

The answer given at the back is $n=9$. So my question is why is $16$ not possible?


1 Answer 1


For $n=16,$ the maximum angle $=120^\circ+(16-1)5^\circ>180^\circ$

But what is Convex Polygon?


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