First slide

Arithmetic progression

Question

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

Difficult

A

8
B

9
C

10
D

16

Solution

From geometry , the sum of all internal angles $= (n - 2) \times 180^{0}$
Where n is the number of sides of the polygon.

$∴ \frac{n}{2} [2 \times 120^{0} + (n - 1) \times 5^{0}] = (n - 2) \times 180^{0}$

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

If n=16 then the $16^{t h}$ internal

Angle = $120^{0} + (16 - 1) \times 5^{0} = 195^{0} > 180^{0}$

$∴ n \neq 16$ . Hence n=9

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App