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a polygon has 27 diagonals.how many sides does the polygon have?(please do it step by step otherwise i can't understand)
Let the number of sides be n and use the formula: (1/2)n(n-3) =
number of  diagonals  = (1/2)n(n-3) = 27

Multiply both sides by 2 and then form a quadratic equation:

n2-3n-54 = 0

Solving the above quadratic equation works out as:

n = -6 or n = 9 Since the sides can't be negative, n = 9

Therefore the polygon has 9 sides.


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