What are the steps for constructing the bisector of an angle using only a compass and a straightedge?

Step 1: Draw an arc from each of these points of intersection so that the arcs intersect in the interior of the angle. The compass needs to stay open the same amount throughout this step.

Step 2: Draw the ray from the vertex of the angle to the intersection of the two arcs drawn during the previous step.

The steps for constructing the bisector of an angle using only a compass and a straightedge are as follows,

Step 1 :

Place the compass on the vertex of the angle.

Step 2 :

Set the compass on the vertex and adjust it to any length.

Step 3 :

Draw arcs on both sides ( rays ) of the angle.

Step 4 :

From the intersection of arcs and sides in both sides draw another arcs ( Without changing the span of compass ) between the sides of the angle such that we get intersection of arcs.

Step 5 :

With help of straightedge, join the vertex and the intersection point we get in previous step.