Abc is an isosceles triangle with angle abc 52 degrees
xy is parallel to bc
work out the size of angle bac
-! : d

We need the picture to answer this question.  From the information
given, we can't be sure that XY is even on the same planet as the
triangle.  We certainly don't know how they're related.

All we can say for sure is that if one angle of an isosceles triangle is
52 degrees, then another one is either 52 degrees or 64 degrees.

Are you asking for 6 or 15?