The interior angles of a polygon are in arithmetic progression. The smallest angle is 120° and the common difference is 5°. Find the number of sides of the polygon.

Correct option is B

Given:

Smallest interior angle (a) = 120°
Common difference (d) = 5°
Number of sides = n

Concept used:
Sum of interior angles of a polygon = (n - 2) × 180°
If angles are in arithmetic progression:
Sum of all interior angles = n/2 × [2a + (n - 1)d]

Formula used:
n/2 × [2a + (n - 1)d] = (n - 2) × 180

Solution:
Substitute a = 120°, d = 5°

n/2 × [240 + 5(n - 1)] = (n - 2) × 180
=> n/2 × (235 + 5n) = 180n - 360
=> 235n + 5n² = 360n - 720
=> 5n² - 125n + 720 = 0
=> n² - 25n + 144 = 0
=> (n - 9)(n - 16) = 0

Hence, n = 9 or 16
For n = 16, largest angle = 120 + (15 × 5) = 195° (>180°), not possible.

Correct answer is (b) 9.