Qstnid -B-16- If The Difference Between The Exterior Angle Of A N Sided Regular Polygon And An (N + 1) Sided Regular Polygon Is 12°, Find The Value Of N. - 16: Understanding Shapes (Including Polygons) Class 8 Maths - Icse-viii-mathematics

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ICSE-VIII-Mathematics

16: Understanding Shapes (Including Polygons) Class 8 Maths

with Solutions - page 5

Qstn# B-16 Prvs-Qstn Next-Qstn

#16
If the difference between the exterior angle of a n sided regular polygon and an (n + 1) sided regular polygon is 12°, find the value of n.
Ans : We know that sum of exterior angles of a polygon = 360°
Each exterior angle of a regular polygon of 360°
sides = 360˚/n
And exterior angle of the regular polygon of (n + 1) sides = 360˚/(n + 1)
∴ 360˚/n - 360˚/(n + 1) = 12
⇒ 360 [1/n - 1/(n + 1)] = 12
⇒ 360[(n + 1 - n)/n(n + 1)] = 12
⇒ (30 × 1)/(n² + n) = 12
⇒ 12(n² + n) = 360˚
⇒ n² + n = 36˚ (Dividing by 12)
⇒ n² + n - 30 = 0
⇒ n² + 6n - 5n - 30 = 0 {∵ -30 = 6 ×(-5) = 1= 6 - 5}
⇒ n(n + 6) - 5(n + 6) = 0
⇒ (n + 6)(n - 5) = 0
Either n + 6 = 0, then n = - 6 which is not possible being negative
Or, n - 5 = 0, then n = 5
Hence, n = 5