Question

Question 18 The difference between any two consecutive interior angles of a polygon is 5°. If the smallest angle is 120°, find the number of the sides of the polygon.

Class X1 - Maths -Sequences and Series Page 186

Answer 1

we know that
Sn = n/2{2a+ (n-1)d}

But for a polygon ,
sum of side angle of polygon {sn} = (n-2)×180°

hence,
(n - 2) × 180° = n/2{2a + (n - 1)d}
here given,
a = 120° , d = 5°
so,
(n - 2) × 180° = n/2{2 × 120° + (n - 1) × 5°}
(n - 2) × 360° = n{ 240° + 5n - 5°}
360n - 720 = 235n + 5n²
5n² + 235n - 360n + 720 = 0
5n² -125n + 720 = 0
n² - 25n + 144 = 0
n² - 16n - 9n + 144 = 0
n(n - 16) -9( n -16) = 0
(n - 9)(n - 16) = 0
n = 9 , 16

but if we take n = 16 then,
T16 = 120 + (16-1) × 5
= 120 + 15 × 5
= 120 + 75 = 195° > 180°.
so, only n = 9 is the required number of sides.

Answer 2

Here u go mate

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