The angles of a polygon are in A.P. with common difference 5°. If the smallest angle is 120°, find the number of sides of the polygon.

Given, angles of polygon are in A.P.,

a = 120° and d = 5°.

Let no. of sides be n and so sum of angles = (2n - 4) × 90°

Sum of A.P. of angles = $\dfrac{n}{2}[2 \times 120° + (n - 1) \times 5°]$

$\therefore \dfrac{n}{2}[2 \times 120° + (n - 1) \times 5°] = (2n - 4) × 90° \\[1em] \Rightarrow \dfrac{n}{2}[240° + 5°n - 5°] = 180°n - 360° \\[1em] \Rightarrow 240°n + 5°n^2 - 5°n = 360°n - 720° \\[1em] \Rightarrow 5°n^2 + 235°n = 360°n - 720° \\[1em] \Rightarrow 5°n^2 - 125°n + 720° = 0 \\[1em] \Rightarrow 5°(n^2 - 25n + 144) = 0 \\[1em] \Rightarrow n^2 - 25n + 144 = 0 \\[1em] \Rightarrow n^2 - 16n - 9n + 144 = 0 \\[1em] \Rightarrow n(n - 16) - 9(n - 16) = 0 \\[1em] \Rightarrow (n - 9)(n - 16) = 0 \\[1em] \Rightarrow n = 9, 16.$

Hence, number of sides = 9 or 16.