Question

In a polygon, the interior angles are in A.P. with common difference $5^{\circ }$ and smallest angle ${120}^{\circ }$, then the number of sides is :

• A. 9 or 16
• B. 16
• C. 9
• D. 25

Answer 1

The correct option is C

9

Let number of sides of polygon = n.

∴ Sum of internal angles = 180n - 360.

∴ 180n - 360 = $\frac{n}{2}$[240 + (n-1)5]

⇒ $n^2$ - 25n + 144 = 0 ⇒ n = 16 or 9.

Since internal angle of a polygon < ${180}^{\circ }$.

$T_{16}$ = 120 + 15 × 5 = 195 > ${180}^{\circ }$ ⇒ n ≠ 16.

Hence n = 9.