Bisect Angle with Compass and Straight Edge
This example demonstrates how to bisect an angle into two equal parts using a compass and straight edge.
Steps

Start with an angle formed between two rays.

Place the point of the compass at the vertex of the two rays and draw a circle of any radius. The bigger the circle the more accurate the result will be.

Place the point of the compass at one of the points along the ray and draw an arc from the other point outwards.

Repeat this process for the other point. Drawing an arc outward that intersects the first arc.

Draw a line fromt the point of intersection to the vertex of the angle.
We have finished dividing the angle into two equal angles.