the angles of a polygon are in AP with common difference 5° . if the smallest angle is 120°, find the number of sides of the polygon.
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No. Of sides =9..... For detail answer visit learncbse. Com there u can find full answer
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Answer:
n= 16,9
SOLUTION:
Suppose the no. of sides of the polygon is n.
Sum of all interior angles of polygon= ( n-2) × 180
lowest angle of polygon, A = 120 degree
Common difference, d = 5
n/2 [ 2A + (n-1) d ] = ( n-2) × 180°
n/2 [ 2×120 + (n-1) ×5 = 180n-360°
n/2 [ 240+ 5n-5] = 180° (n-2)
n [235+5n] = 360° (n-2)
235n+5n^2 = 360°(n-2)
5n [ 47+n] = 360°(n-2)
n[ 47+ n] = 72° (n-2)
n^2 +47n = 72n-144
n^2 +25n + 144 =0
n^2-9n-16n+144=0
n( n-9)-16(n-9) =0
n=16, n=9
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