Question

30. Two regular polygons are such that the ratio between their number of sides is 1:2 and the ratio of measures of there interior angle
interiorangles is 3:4.Find thenumber of sides of each polygon. /दो समबहुभुजों की भुजाओं की संख्या का अनुपात 1:2 है तथा उनके
अंतःकोणों का अनुपात 3:4 है। प्रत्येक बहुभुज की भुजाओं की संख्या ज्ञात करें।​

Answer 1

5 & 10

first polygon sides = m

second polygon sides = n

sides ratio = 1 : 2

hence ...

m = 2n

now.....

first polygon interior angle : 180 (n - 2)/n

second polygon interior angle : 180 (m - 2)/m

angle ratio = 3 : 4

[ 180 (n - 2)/n ] / [ 180 (m - 2)/m ] = 3 / 4

[ (n - 2)/n ] / [ (2n - 2)/2n ] = 3 / 4

(n - 2) / (n - 1) = 3 / 4

4 ( n - 2 ) = 3 ( n - 1 )

n = 5

but m = 2n = 2 (5) = 10

therefore the polygons are Pentagon (5) & Decagon (10)