Thank you for reporting, we will resolve it shortly
Q.
The internal angles of a convex polygon are inA.P. The smallest angle is $120^{\circ}$ and the common difference is $5^{\circ}$. The number to sides of the polygon is
From geometry, the sum of all internal angles $=(n-2) \times 180^{\circ}$
where $n$ is the number of sides of the polygon.
$\therefore \frac{n}{2}\left[2 \times 120^{\circ}+(n-1) \times 5^{\circ}\right]=(n-2) \times 180^{\circ} $
$\Rightarrow n^{2}-25 n+144=0$
$ \Rightarrow (n-16)(n-9)=0$
If $n=16$ then the $16^{\text {th }}$ internal angle
$=120^{\circ}+(16-1) \times 5^{\circ}=195^{\circ}>180^{\circ}$
$\therefore n \neq 16$. Hence $n=9$