Given an angle with vertex at A
Step 1. Scribe an arc centered at A and intersecting the arms of the angle at B and C.
Step 2. On the other line, scribe and arc of the same radius centered at A' intersecting the line at B'
Step 3. Use the compass to measure the distance from B to C, and with the compass centered at B' scribe an arc whose radius is the distance from B to C intersecting the arc from Step 2 at C'.
Step 4. Draw the line from A' through C'.