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CBSE Class 8 Answered

The exterior angle of regular polygon is 1/3 of its interior angle.find the number of side of polygon ??      Ans -8 sides
Asked by Mohdayaz9921 | 30 Dec, 2018, 06:48: AM
answered-by-expert Expert Answer
sum of interior and exterior angles = 180°
 
since the ratio is 1:3, let exterior angle be x and interior angle be 3x.
 
then x+3x = 4x = 180 or x = 45
 
hence interior angle = 135°
 
if n is number of sides of regular polygon, interior angle θ is given by :   begin mathsize 12px style fraction numerator n minus 2 over denominator n end fraction cross times 180 space equals space theta end style ......................(1)
hence sunstituting θ = 135 in eqn.(1), and solving for n, we get n = 8
 
hence number of sides of regular polygon is 8
Answered by Thiyagarajan K | 30 Dec, 2018, 08:42: AM
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