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CGP EDU Academic Team
Published on: August 14, 2026
The interior angles of a polygon are in A.P. The smallest angle is 120º & common difference 5º. Find no. of sides of polygon
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Sol. Let no. of sides of polygon in 'n'
∴ Sum of n angle of polygon is = (n – 2) × 180 ….(1)
Also given smallest angle = 120º & common difference = 5º
∴ sum of angles of polygon = 
[240 + (n – 1)5]…(2)
From (1) & (2)
(n – 2) 180 = 
(n – 2) 36 = 
[n + 47]
(2n – 4) 36 = n 2 + 47n
n 2 – 25n + 144 = 0
⇒ n = 9, 16
At n = 16
∴ Largest angle will be = 120 + 15 × 5 = 195 Not true
∴ n = 9
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