Find the angle between a line trending 124, plunging 40, and a second line trending 038, plunging 50.
1. Plot the first line. In this case we have rotated the reference (north) mark 34 degrees to the west and plotted the point (red) on the equator (34 + 90 = 124). We count in 40 degrees from the primitive circle.
2. Plot the second line. Here we have rotated the reference (north) mark 38 degrees to the west and plotted the point (green) on the north-south meridian. We count in 50 degrees from the primitive circle.
3. Rotate the overlay so the two points lie on a common great circle (purple). Count the degrees along the circle.
4. Rotate the overlay to its original position.
Note in Figure 3 that we could also have counted in the other direction. We could have counted from point 1 to the south pole of the diagram, then come in at the north pole and continued counting to point 2. In that case, we would have gotten 124 degrees, or 180-56. Either result would be correct.