How can I calculate the apparent dip of a plane from another orientation in Dips?

To calculate the apparent dip of a plane, add the plane to the stereonet using the Add Plane option.  Then use the Add Line option in the Tools menu to add a line at the desired orientation.  The intersection of the great circle and the line will give you the apparent dip, which you can measure graphically.  To get the coordinates, hover the mouse over the intersection point, and make sure that the Convention option for coordinate (click on the box in the lower right corner of the stereonet) is set to Trend/Plunge, so that the coordinates of the intersection line are displayed in Trend/Plunge format.