There angle bisector is the half-line passing through the vertex of the angle as you can see in the drawing below and which divides this angle into two angles of the same measure.
Another definition:
There bisector of an angle is the half-line which divides the angle into two adjacent angles of the same measure.
We can construct the bisector either with a protractor by tracing the two angles of the same measure either with a compass by drawing a point A and a point B equidistant from “O” then starting from points A and B we draw two arcs of a circle which intersect at C