it would be good to show which angles you are doing
the first line, you are starting with the fact that since ABC is a striaight angle, therefor ABY+YBC=180, so then (x+25)+(2x+50)=180, slving for x, we get x=35 like you did
remember that if AC and DF are parallel, then YBC has the same angle measure as BEF
so find YBC and BEF
we know x=35 so subsitute
2(35)+50=5(35)-55?
70+50=175-55?
120=120?
true
they are paralell
