Draw the known angles on the diagram to identify those with measures equal to 35º:
Since the line BA is tangent to the circle, then the angle BAC is a right angle.
Since the arc CD measures 125º, so does the angle DOC. The angle BOA is suplementary to DOC, then it measures 55º. The angle ABO is complementary to BOA, then it measures 35º.
On the other hand, the angle BCO is complementary to ABC, then it measures 35º.
Therefore, the angles ABO and BCO have measures equal to 35º.