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)
⇒

n

2

[2×120°+(n−1)5°] = 180° (n - 2)
⇒ 240n + 5n2 – 5n = 360 (n – 2) ⇒ 5n2 + 235n – 360n + 720 = 0
⇒ 5n2 – 125n + 720 = 0 ⇒ n2 – 25n + 144 = 0 ⇒ n2 – 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.