Question

The interior angle of a convex polygon are in AP. The smallest angle is $120$ & the common difference is $5$. Find the number of sides of the polygon -

• A. $9$
• B. $16$
• C. $12$
• D. None of these

Answer 1

Answer: (A), (B)

The correct options are
A $9$
B $16$

Interior Angle sum = $(n-2)\times {180}^{\circ }$

$a=120d=5$

$S_n=\frac{n}{2}\left[2\right(120)+(n-1\left)5\right]$

$\Rightarrow (n-2)\times 180=\frac{n}{2}[240+5n-5]$

$\Rightarrow 360(n-2)=n[235+5n]$

$\Rightarrow 360n-720=235n+5n^2$

$\Rightarrow 5n^2-125n+720=0$

$\Rightarrow n^2-25n+144=0$

$\Rightarrow (n-16)(n-9)=0$

so $n=9$ or $n=16$