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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?

 Sep 2, 2024
 #1
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The number of diagonals of a   n-gon equals :    n (n-3)/2  

so: 

n (n-3)/2 = 2n     Solve for n 

n^2 - 3n = 4n 

n^2 - 7n = 0 

n(n-7) = 0              shows  n = 7    sides 

 Sep 2, 2024

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