Yet another way to look at it : If AB is ll to CD, then angles APE and CQF are congruent, being 180 degrees as given.
This means that Angle CQF must be 70 degrees by the supplementary angle theorem.
This leaves the measurement of FQD to be 110 degrees, and being bisected by ray QR, means that the measurement of angle FQR is 55 degrees, 1/2 of FQD.
Now add m <FQR and m<CQF and you get A) 125 degrees.