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CBSE Class 8 Answered

The ratio of interior angle to the exterior angle of a regular polygon is 5:1, find the number of sides ?      Ans -12
Asked by Mohdayaz9921 | 29 Dec, 2018, 10:28: AM
answered-by-expert Expert Answer
Let x be the interior angle. Hence exterior angle = (180-x)
 
we are given that   x : (180-x) = 5:1   hence begin mathsize 12px style fraction numerator x over denominator 180 minus x end fraction space equals space 5 space space o r space 900 space minus 5 x space equals space x space space o r space space x space equals space 150 end style
hence interior angle is 150°.
 
if a regular polygon has n sides, then interior angle = [(n-2)×180] / n  = 150 ...............(1)
By solving eqn.(1), we get n = 12
Answered by Thiyagarajan K | 29 Dec, 2018, 11:46: AM

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