Sequences and Series · Question 51

JEE Main 2025 (Online) 28th January Evening ShiftNumericalEasy📈 Topic in 55% papers+4

The interior angles of a polygon with n sides are in an A.P. with common difference 6 . If the largest interior angle of the polygon is 219 , then n is equal to .

Answer

Solution

Taking the angles from the largest, they form an A.P. with first term 219 and common difference -6 .

Sum = n2[2(219) - 6(n - 1)] = n(222 - 3n)

Sum of interior angles = (n - 2) 180

222n - 3n2 = 180n - 360

3n2 - 42n - 360 = 0

n2 - 14n - 120 = 0

(n - 20)(n + 6) = 0 n = 20

(Check: smallest angle = 219 - 19 6 = 105 > 0.)

Answer: 20

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