First slide

Arithmetic progression

Question

In a polygon, the interior angles are in A.P. with common difference $5^{0}$ and smallest angle $120^{0}$ , then the number of sides is:

Moderate

A

$9 o r 16$
B

$16$
C

$9$
D

None

Solution

Let the number of sides of polygon $= n$
$∴$ Sum of internal angles $= 180 n - 360$

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

$\Rightarrow$ $n^{2} - 25 n + 144 = 0$ $\Rightarrow n = 16 o r 9$

Since internal angle of a polygon $< 180^{0} .$

$T_{16} = 120 + 15 \times 5 = 195 > 180^{0} \Rightarrow n \neq 16$

Hence $n = 9$

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