Lines AC and DF are parallel if Angles YBC and BEF are equal to each other and/or Angles ABY and YBC = 180 and/or Angles ABY and BEF = 180. So you'd do just that.
2x + 50 = 5x -55. By subtracting 2x from both sides and adding 55 to both sides, you get 3x = 105. x = 35.
Showing that 2(35) + 50 = 120 and 5(35) - 55 = 120 is enough to show that they are parallel.
Also another way would be adding x+25 and 2x + 50 and setting them equal to 180 like you did. OR as mentioned, 2x + 50 is the same angle as 5x - 55 so you can add 5x - 55 and x + 25 and set them equal to 180.