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Let its sides be x and rearrange the diagonal formula into a quadratic equation:-

So: 0.5(x^2-3x) = 252

Then: x^2-3n-504 = 0

Solving the quadratic equation: gives x a positive value of 24

Therefore the polygon has 24 sides irrespective of it being irregular or regular

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Q: How many sides does an irregular polygon have if it has 252 diagonals showing work?
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