After doing this	Your work should look like this
Start with a angle BAC that we will copy.
1.  Make a point P that will be the vertex of the new angle.
2.  From P, draw a ray PQ. This will become one side of the new angle. This ray can go off in any direction. It does not have to be parallel to anything else. It does not have to be the same length as AC or AB.
3.  Place the compass on point A, set to any convenient width.
4.  Draw an arc across both sides of the angle, creating the points J and K as shown.
5.  Without changing the compass width, place the compass point on P and draw a similar arc there, creating point M as shown.
6.  Set the compass on K and adjust its width to point J.
7.  Without changing the compass width, move the compass to M and draw an arc across the first one, creating point L where they cross.
8.  Draw a ray PR from P through L and onwards a little further. The exact length is not important.
Done. The angle ∠RPQ is congruent (equal in measure) to angle ∠BAC.

Proof

This construction works by creating two congruent triangles. The angle to be copied has the same measure in both triangles

The image below is the final drawing above with the red items added.

Constructions pages on this site

Lines

• Introduction to constructions
• List of printable constructions worksheets
• Copy a line segment
• Parallel line through a point
• Perpendicular bisector of a line segment
• Perpendicular from a line at a point
• Perpendicular from a line through a point
• Perpendicular from endpoint of a ray
• Divide a segment into n equal parts

Angles

• Bisecting an angle
• Copy an angle
• Construct a 30° angle
• Construct a 45° angle
• Construct a 60° angle
• Construct a 90° angle (right angle)
• Constructing  75°  105°  120°  135°  150° angles and more

Triangles

• Copy a triangle
• Isosceles triangle, given base and side
• Isosceles triangle, given base and altitude
• Equilateral triangle
• Triangle medians
• 30-60-90 triangle, given the hypotenuse
• Triangle, given 3 sides (sss)
• Triangle, given one side and adjacent angles (asa)
• Triangle, given two sides and included angle (sas)
• Incircle of a triangle
• Circumcircle of a triangle

Triangle Centers

• Triangle incenter
• Triangle circumcenter
• Triangle orthocenter
• Triangle centroid

Circles, Arcs and Ellipses

• Finding the center of a circle
• Circle given 3 points
• Tangent at a point on the circle
• Tangents through an external point
• Focus points of a given ellipse

Polygons

• Hexagongiven one side
• Hexagon inscribed in a given circle
• Pentagon inscribed in a given circle

Non-Euclidean constructions

• Construct an ellipse with string and pins
• Find the center of a circle with any right-angled object