Construction #2 Copy an Angle
To see a video of Mr. Ochs doing examples
Mr Ochs Video To see and example done in flash click on a link below Math Open Ref Math is Fun 

Given an angle, construct an angle congruent to the given angle
Construct an angle XYZ congruent to the given angle ABC
1) With your straight edge, draw a ray for the 1st side of the new angle
2) Choose any radius for the compass
(just remember the larger the radius the better the construction)
3) With this radius place your compass pointer on the vertex of the original angle and then strike an arc that passes through both sides of the angle.
(you don’t need to use A or C)
4) Keeping the same radius move the pointer to the new ray, then with the pointer on the vertex of the new angle strike an arc, starting from on the ray, bigger that the original angle.
5) Go back to the original angle and set the compass radius equal to the distance between the points where the arc intersects the two sides of the angle
6) Keeping the same radius move back to the new angle, then place the pointer on the intersection of the ray and the 1st arc drawn. Now strike another arc that intersects the 1st arc drawn
7) With your straight edge draw a ray from the vertex of the new angle through the point where the two arcs intersect each other