Question

Interior angles of a polygon is in AP. If the smallest angle is 120 and common difference is 5. The. Find the no. Of sides of polygon.



Thanks

Answer 1

JiAnswer(s)

Smallest angle=120degree

Common difference=5

A P is 120, 125, 130,……..

The sum of interior angles of a polygon= (n-2)180

Hence Sum of n terms of an A P = (n-2)180

n/2 {2.120+(n-1)5} = 180(n-2)

5n^2 -125n +720 = 0

n^2 -25n +144=0

n=9 or 16

hence number of sides can be 9 or 16

 

Answer 2

Answer:

Either 9 or 16 sides.

Step-by-step explanation:

Let n be the number of sides.

The sum of n values from an AP with common difference d and starting at a is given by the formula

na + n(n-1)d/2.

We have a = 120 and d = 5, so the sum of the angles is

sum of angles = 120 + 125 + 130 + ... = 120n + 5n ( n - 1 ) / 2.

We also know that the sum of the angles in a polygon with n sides is

( n - 2 ) × 180 degrees.

As we have two expressions for the same thing (the sum of the angles), this gives us an equation for n

120n + 5n ( n - 1 ) / 2 = 180 ( n - 2 )

=> 240n + 5n² - 5n = 360n - 720

=> 5n² - 125n + 720 = 0

=> n² - 25n + 144 = 0

=> ( n - 9 ) ( n - 16 ) = 0

=> n = 9 or n = 16