The difference between any two consecutive interior angles of a polygon is 5°. If the smallest angle is 120°, find the number of the sides of the polygon.

Asked by Abhisek | 1 year ago |  100

##### Solution :-

It’s understood from the question that, the angles of the polygon will form an A.P. with common difference d = 5° and first term a = 120°.

And, we know that the sum of all angles of a polygon with n sides is 180° (n – 2).

Thus, we can say

sn = 180° (n – 2)

$$s_n=\dfrac{n}{2}[2a+(n-1)d]$$

= 180° (n – 2)

$$=\dfrac{n}{2}[240°+(n-1)5°]$$

= 180° (n – 2)

= n[240+5n−5]=360(n−2)

= 240n+5n2−5n=360n−720

= 5n2−125n+720=0

= n2−25n+144=0

= (n−9)(n−16)=0

n = 9,16

Therefore, the number of the sides of the polygon 9 or 16 .

Answered by Pragya Singh | 1 year ago

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