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Q.

The interior angles of a polygon are in A.P. The smallest angle is 120°  and the common difference is 5° . Then the number of sides of the polygon is

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a

answer is I.

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Detailed Solution

n2[2(120)+(n−1)5]=(2n−4)90°

n[240+5n−5]=(2n−4)180

240n+5n2−5n=360n−720

5n2−365n+240n+720=0

⇒5n2−125n+720=0

⇒n2−25n+144=0

(n−16)(n−9)=0

⇒n=16  (or) 9.

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