Question

The interior angles of a convex polygon are in AP. The smallest angle is ${120}^o$ & the common difference is $5^o$. Find the number of sides of the polygon.

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

Answer 1

The correct option is D None of these

$a={120}^{\circ },d=5^{\circ }\left(\because given\right)\underset{–}{Sn}=\frac{n}{2}\left[24+\left(n-1\right)\times d\right]{360}^{\circ }=\frac{n}{2}\left[2\times {120}^{\circ }+\left(n-1\right)\times 5^{\circ }\right]\left[\because adationofallintenicanglesofpolygon={360}^{\circ }\right]360\times 2=n\left[240+5n-5\right]=240n+5n^2-5n360\times 2=235n+5n^{2}5n^2+235n-360\times 2=0n^2+47n-72\times 2=0\begin{array}{c}n=2.8\\ n=-49.8865\end{array}\to Noneoftheseoption.$