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ICSE Class 9 Answered

The number of sides of two regular polygon are in the ratio 4:5 and their interior angles are in the ratio 15:16.Find the numbers of sides of each of the polygon. .
Asked by Kushal152002 | 26 Feb, 2018, 10:31: PM
answered-by-expert Expert Answer
begin mathsize 16px style if space there space are space straight n space sides space
then space interior space angles space equals fraction numerator open parentheses straight n minus 2 close parentheses cross times 180 over denominator straight n end fraction
let space straight x space and space straight y space are space number space of space sides
straight x over straight y equals 4 over 5
interior space angles space equals fraction numerator open parentheses straight x minus 2 close parentheses cross times 180 over denominator straight x end fraction
interior space angles space equals fraction numerator open parentheses straight y minus 2 close parentheses cross times 180 over denominator straight y end fraction
fraction numerator fraction numerator open parentheses straight x minus 2 close parentheses cross times 180 over denominator straight x end fraction over denominator fraction numerator open parentheses straight y minus 2 close parentheses cross times 180 over denominator straight y end fraction end fraction equals 15 over 16
fraction numerator open parentheses straight x minus 2 close parentheses cross times 180 over denominator open parentheses straight y minus 2 close parentheses cross times 180 end fraction cross times straight y over straight x equals 15 over 16
fraction numerator open parentheses straight x minus 2 close parentheses cross times 180 over denominator open parentheses straight y minus 2 close parentheses cross times 180 end fraction cross times 5 over 4 equals 15 over 16..... put space straight x equals fraction numerator 4 straight y over denominator 5 end fraction
fraction numerator open parentheses fraction numerator 4 straight y over denominator 5 end fraction minus 2 close parentheses over denominator open parentheses straight y minus 2 close parentheses end fraction equals 3 over 4
solve end style
Answered by Arun | 27 Feb, 2018, 10:53: AM
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