The angle in one regular polygon is to that in another as 3:2 and the number of sides in first is twice that in second. Determine the number of sides of two polygons.

1
by simple

2014-10-14T18:46:36+05:30

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Angle at the center of polygon = 360°.
If you divide the polygon by drawing lines from n vertices to center, it will split into n isosceles triangles.
The angle at the center in each triangle = Ф = 360°/n

The angle at each vertex inside the polygon = 2 (180 - 360°/n)
A  = 360° (1 - 2/n) = 360° (n - 2) / n

Now let us say the two polygons P1 and P2 have number of sides as 2N and N respectively.

Angle in P1 : angle in P2  = 360°(2N-2)/2N : 360°(N-2)/N = 3 : 2
so
(N - 1) / ( N - 2 ) = 3/2
2 N -2 = 3 N  - 6
N = 4

So the polygons have 8 sides and 4 sides respectively.