SOLUTION: The number of diagonals in a certain regular polygon is equal to 2 times the number of sides. How many sides does this polygon have?

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Question 1210521: The number of diagonals in a certain regular polygon is equal to 2 times the number of sides. How many sides does this polygon have?
Answer by ikleyn(53763) About Me  (Show Source):
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The number of diagonals in a certain regular polygon is equal to 2 times the number of sides.
How many sides does this polygon have?
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Let n be the number of sides.

The number of diagonals is then  %28n%2A%28n-3%29%29%2F2.


From the problem, we have this equation

    %28n%2A%28n-3%29%29%2F2 = 2n.


It implies

    %28n-3%29%2F2 = 2,

    n-3 = 4,

     n = 4 + 3 = 7.


ANSWER.  The number of sides is 7.


CHECK.  The number of diagonals is  %287%2A%287-3%29%29%2F2 = %287%2A4%29%2F2 = 7*2 = 14.   ! correct !

Solved.