So AIB is 109 degrees. IAB + IBA + 109 = 180, so IAB + IBA = 180 -109 = 71.
AX and BY are angle bisectors so IAB = CAB/2, and IBA = CBA/2. (CAB + CBA)/2 = 71.
Rearrange the last equation and you should be very close to your answer.
If you don't understand anything, feel free to ask!