I think that most surgeons, or their offices, will tell you, since they often measure it from x-rays taken during or after surgery, and it is likely to be written in the surgical record.
Just for fun, I did measure mine off of my x-ray, and came out within one degree of what Dr. Gross confirmed that it was. I came up with around 40 degrees, and he confirmed that it was 39.
I used the same approach mentioned earlier. I drew a line connecting across two matching points on each side of the pelvis, in order to establish the true horizontal, and then drew a line along the flat lower edge of the cup, and extended it until it intersects the first line. (You may need to be able to draw on a surface that is larger than the X-ray). Then just measure that intersection angle, which gives you the angle of abduction. The more vertical your cup, the more that number would be greater than 45 degrees, the less vertical the cup, it may be less than 45. It could be argued that if you have any rotations in or around the pelvis, the horizontal line may be off a little, but it should be a pretty close reference.