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(#M40010145) BOOK question Keep an EYE

The difference between any two consecutive interior angles of a polygon is 5 degree. If the smallest angle is 120 degree , How many sides the polygon have ?

Asked In Book Devendra Marghade (12 years ago)

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Garima  (12 years ago)

Sum of internal angle and external angle at any vertex of polygon is 180 deg.

So largest exterior angle = 180-20= 60 deg.
Sum of all external angles = 360 deg

so external angles are 60,55,50,45,40,35,30,25,20 deg.

hence 9 angles.
so polygon has 9 sides.

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jyotish r  (12 years ago)

the polygon have 9 sides

(n-2)180=120+125+..n terms=n/2(240+5n-5)

180n-360=117.5n+2.5n^2

2.5n^2 - 62.5n +360=0

solving,
n=9 is the answer.

(We must discard the n=16 solution, because if n=16, the angles go past 180, and you can't have a 180 degree angle as an interior angle in a polygon)

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