<PRE><B>Question 265363</B>
How many diagonals does a regular n-gon have?
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The n-gon will have n vertices.
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Every pair of vertices determines a line segment.
You have nC2 = n(n-1)/2 pairs of vertices.
So you have n(n-1)/2 line segments determined.
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n of those line segments are sides of the n-gon.
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So the number of diagonals is [n(n-1)/2] - n 
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Cheers,
Stan H.</PRE>