Question
The ratio between the number of sides of two regular
polygon is 2:5 and the ratio between their interior angles is 10:12. The number of sides of these polygons are respectively:Solution
Let number of side of first polygon = 2x & that of 2nd polygon = 5x ; then ratio of their interior angles = I(1): I(2) = 10:12 or (180 - E1):(180-E2) = 10:12 or 2160 - 12E1 = 1800 - 10E2 or 12E1 - 10E2 = 2160 - 1800 = 360 or 12(360/2x) - 10(360/5x) = 360 or 2160/x - 720/x = 360 or 1440/x = 360 or x = 1440/360 = 4
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