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Let n be the number of sides:

1/2*(n2-3n) = diagonals

1/2*(n2-3n) = 902

Multiply both sides by 2 and form a quadratic equation:

n2-3n-1804 = 0

Solving the above by means of the quadratic equation formula gives a positive value for n as 44

Therefore the polygon has 44 sides

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Q: How many sides does a polygon have if it has 902 diagonals?
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