Although I can't physically help you with the construction, I can guide you through the steps! Here's how you can construct the angle bisector of angle ABC:
1. Draw a line segment AB.
2. Place the compass at point B and draw an arc that intersects both sides of angle ABC.
3. Without changing the compass width, place the compass at point C and draw another arc that intersects the previous arc.
4. Label the points where the arcs intersect as D and E.
5. Draw a straight line from point B to point D, and another line from point B to point E.
6. The line segment that passes through point B and bisects angle ABC is the angle bisector.
Remember to be precise and accurate with your constructions!