Let there are n sides of a polygon. Then sum of all interior angles = 180° (n – 2) ....(i) We have given smallest angle = 120° and other angles are 125°, 130°, 135°,......, [120° + (n – 1)5°] and this forms an A.P. From (i), we have, 120° + 125° +.........+ [120° + (n – 1)5°] = 180° (n – 2) ⇒ $\frac{n}{2}\left[2\times120^{\circ}+(n-1)5^{\circ}\right]$ = 180° (n - 2) ⇒ 240n + $5n^{2}$ – 5n = 360 (n – 2) ⇒ $5n^{2}$ + 235n – 360n + 720 = 0 ⇒ $5n^{2}$ – 125n + 720 = 0 ⇒ $n^{2}$ – 25n + 144 = 0 ⇒ $n^{2}$ – 16n – 9n + 144 = 0 ⇒ (n – 16) (n – 9) = 0 ⇒ n = 16 or n = 9 n ≠ 16 Since If n = 16 then the angle will be 120° + 15·5° = 120° + 75° = 195° > 180°, which can not be possible. Hence n = 9.