compass and straightedge construction of duplicating an angle
In all of the pictures supplied, the angle in red is the one that is to be duplicated.
One can duplicate an angle using compass and straightedge as follows:

1.
Draw one of the rays of the new angle.

2.
With one point of the compass at the vertex (http://planetmath.org/Vertex5) of the given angle, draw an arc that intersects both of its rays.

3.
With one point of the compass at the point where the vertex of the new angle is supposed to be, draw an arc that intersects the ray of the new angle and extends far from the ray in one direction. The compass needs to be open the same amount as it was in the previous step.

4.
Use the compass to the distance between the two points of intersection of the given angle and its arc. This length needs to be used in the next step.

5.
With one point on the intersection of the ray of the new angle and its arc, draw an arc so that it intersects the other arc that was drawn for the new angle.

6.
Draw the ray from the vertex of the angle to the intersection of the two arcs.
If you are interested in seeing the rules for compass and straightedge constructions, click on the provided.
Title  compass and straightedge construction of duplicating an angle 
Canonical name  CompassAndStraightedgeConstructionOfDuplicatingAnAngle 
Date of creation  20130322 17:13:20 
Last modified on  20130322 17:13:20 
Owner  Wkbj79 (1863) 
Last modified by  Wkbj79 (1863) 
Numerical id  11 
Author  Wkbj79 (1863) 
Entry type  Algorithm 
Classification  msc 51M15 
Classification  msc 5100 
Synonym  compass and straightedge construction of copying an angle 
Defines  duplicating an angle 
Defines  copying an angle 
Defines  duplicate an angle 
Defines  copy an angle 
Defines  duplicate the angle 
Defines  copy the angle 