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 the second. Determine the number of sides of two polygons.

Explanation

Let `n` and `m` be the number of sides in two regular polygon respectively. We know that each angle of `n` - sided regular polygon is `frac{(2 n-4)}{n}` angles.


Now,


According to the question,



`frac{(frac{2 n-4}{n}) times 90^{circ}}{(frac{2 m-4}{m}) times 90^{circ}}=frac{3}{2}`


`Rightarrow quad frac{(2 n-4) m}{(2 m-4) n}=frac{3}{2} ldots text { (i) }`



Also,


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