Two regular polygons are such that the ratio between their number of sides is 1 2 and the ratio of m...........

Quantitative Aptitude (CGL) Mensuration 3D

Two regular polygons are such that the ratio between their number of sides is 1:2 and the ratio of measures of their interior angles is 3:4. Then the number of sides of each polygon are

10, 20

4, 8

3, 6

5, 10

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Explanation:

Number of sides of Reg Polygon1 = x
=> number of sides of Reg Polygon2 = 2x
Each interior angle of P1 = 3y
=> Each interior angle of P2 = 4y
Since Each interior angle = {(n-2)* 180}/n
=> 3y = (x-2)*180 /x ……………….(1)
& 4y = (2x-2)*180 /2x ……………..(2)
Now, solve the above pair of equations
We get,
360x - 720 = 6xy …………. (1)
360x -360 = 8xy ………….. (2)
=> 360 = 2xy
=> xy = 180
Plug in the above value in eq(1)
360x -720 = 6 * 180
=> 360x = 1080 +720
=>360 x = 1800
=> x = 5
So, P1 is regular pentagon ( 5 sides)
& P2 is regular decagon (10 sides)