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Your question is quite confusing because you used the phrase 'two polygon'. When asking mathematical or geometrical questions about shapes you ask about a single specific thing . I assume you meant to ask, '----number of sides of various different polygons, given the number of diagonals in each of them.' I have been drawing polygons with 5 and 6 and 7 and 8 sides and discovering the number of diagonals which can be drawn inside each of them , does not seem to follow a simple formula. I will look into it further and see if I can post you an answer in a day or two. Very interesting question I must say. Hope I can solve it .

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The diagonal formula for any polygon is: 1/2*(n2-3n) = number of diagonals

Rearrange the formula into a quadratic equation and solve it for a positive value which will be the number of the sides of the given polygon

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Q: How do you find the number of sides of two polygon given the number of diagonals?
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