# 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.

Smallest Angle = 120°

Difference between any two consecutive interior angles of a polygon = 5°

The angles of the polygon will form an A.P. with common difference d as 5° and first term a as 120°.

We know, sum of all angles of a polygon with n sides = 180° (n – 2)

Sn = 180° (n – 2) Equating both we get  n (240 + 5n – 5) = 360n – 720

5n2 + 240n – 5n – 360n + 720 = 0

5n2 - 125n + 720 = 0

n2 – 25n + 144 = 0

n2 – 16n – 9n + 144 = 0

n (n – 16) – 9 (n – 16) = 0

(n – 9) (n – 16) = 0

n = 9 or 16

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