Question
The ratio between the number of sides of two regular
polygon is 1 : 3 and the ratio between their interior angles is 3 : 4. The number of sides of these polygons are respectively:Solution
Let number of side of first polygon = x & that of 2nd polygon = 3x ; then ratio of their interior angles = I(1): I(2) = 3:4 or (180 - E1):(180-E2) = 3:4 or 720 - 4E1 = 540 - 3E2 oe 4E1 - 3E2 = 720 - 540 = 180 or 4(360/x) - 3(360/3x) = 180 or 1440/x - 360/x = 180 or 1080/x = 180 or x = 1080/180 = 6
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