The difference between any two consecutive interior angles of a polygon is 5⁰. If the smallest angle is 120⁰, find the number of the sides of the polygon.

We know that if the number of sides is n, then the sum of interior angles of a polygon with

n sides = (2n - 4) right angles

           = (180n- 360) degrees

Now the sequence of angles

120°, 125°, 130°,... form an A.P. with a = 120°, d = 5°

Sn =

⇒ 180n – 360 =
or 2(180n – 360) = n[240 + 5n - 5)]

or 360n - 720 = 240n + 5n² + 5n

or 5n² – 125n + 720 = 0

or n² - 25n + 144 =0

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

or n = 9, 16

But n = 16 is not possible as it gives the last term of A.P.

        = a + (n - 1)d

        = 120 + (16-9) x 5

        = 195°

Thus the number of sides = 9.