Question

The interior angles of a convex polygon are in $A.P$. The smallest angle is ${120}^0$ and the common difference is $5^0$. The number of sides is

• A. $7$
• B. $16$
• C. $9$
• D. $9$ or $16$, both values being permissible.

Answer 1

Answer: (D)

$9$ or $16$, both values being permissible.

sum of all interior angles in polygon is (n-2)180

according to question the angles are in AP

120,125,130........

sum of n terms in AP =(n-2)180

$\frac{n}{2}(240+(n-1\left)5\right)=(n-2)180$

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

by solving this we get n=16,9