Polygons

The formula for the number of diagonals in a polygon with sides is given by: We are given that the number of diagonals is 54. So, we set up the equation: Multiplying both sides by 2: Expanding the equation: Rearranging the equation: Solving this quadratic equation using the quadratic formula: Thus, we get two solutions: Since the number of sides must be positive, we choose .

The correct option is (D):