The number of diagonals in a certain regular polygon is equal to two times the number of sides. How many sides does this polygon have?
Number of diagonals in a polygon is given by :
n ( n-3) / 2 where n = the number of sides
So
n ( n- 3) / 2 = 2n simplify
n (n -3) = 4n
n^2 - 3n = 4n
n^2 - 7n = 0
n ( n - 7) = 0
Setting each factor to 0 and solving for n produces
n = 0 reject
n = 7
