The number of sides of two regular polygons are as 5: 4 and the difference between their angles is `9^@.` Find the number of sides of the polygons

Explanation

Let `n` be the Greatest Common Divisor (GCD) of the numbers under the question.
Then one polygon has 5 n sides, while the other has `4 n` sides.


It is well known fact that the sum of exterior angles of each (convex) polygon is `360^{circ}`.
So, the exterior angle of the regular 5 n-sided polygon is `frac{360^{circ}}{5 {n}}`.


Similarly, the exterior angle of the regular `4 {n}`-sided polygon is `frac{360^{circ}}{4 {n}}`.
The difference between the corresponding exterior angles is `9^{circ}`.



`Rightarrow frac{360^{circ}}{4 n}-frac{360^{circ}}{5 n}=9^{circ}`


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