If point O lies in the interior of angle ABC, and the measure of angle OBC + the measure of angle ABO equals the measure of angle ABC, then point O is located on the angle bisector of angle ABC.
This is because the sum of the angles around point O within angle ABC equals the entirety of angle ABC itself, indicating that O effectively divides angle ABC into two angles (OBC and ABO) that together measure the same as angle ABC. By the properties of angle bisectors, this division suggests that O symmetrically reflects the measures of the angles on either side, aligning it precisely as the angle bisector.