The whole parallelogram is 360. The two obtuse angles are each 71+45=116, which adds up to 232.
The two acute angles together add up to 360 (the whole parallelogram) minus 232 (the two obtuse angles), which is 128. The two acute angles are equal in a parallelogram, so you can divide 128 by 2 to get one of the angles, which is 64.
This means that angle BAD is 64. BAD is just the sum of BAC and CAD, so you can now figure out BAC:
BAD=BAC+CAD
64=BAC+27 (the 27 is given)
BAC=64-27
BAC=37
