Geometry

 

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?    

 

The number of diagonals in a regular polygon with "n" sides is calculated using the formula: n(n-3) / 2.    

 

             from the formula                                d  = n • (n – 3) / 2    

 

             given                                                  d  =  2 • n    

 

                                                                      2n  =  n • (n – 3) / 2   

 

                                                                      2n  =  (n² – 3n) / 2     

 

                                                                      4n  =  n² – 3n    

 

                                                                        n²  =  7n    

 

                                                                         n  =  7    

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