A polygon has 405 diagonals determine its number of sides
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Answer:
30 sides
Step-by-step explanation:
Let n be the number of sides.
Number of diagonals is n(n-3)/2.
So...
n(n-3)/2 = 405
=> n(n-3) = 810
=> n² - 3n - 810 = 0
=> ( n + 27 ) ( n - 30 ) = 0
=> n = -27 or n = 30
=> n = 30 (can't have a negative number of sides!)
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