Hi Dale, good question!

I had forgotten about how to do this since I normally interactively transform objects using the mouse.

Xara can remember the rotation of any "Smart Shape" (an object drawn with the Rectangle, Ellipse, or QuickShape tools).

The example below shows an ellipse which I rotated clockwise interactively using the mouse. The ellipse object was then selected and the Ellipse Tool was made active. Now if you look in the Info Bar and select "Rotation" from the drop-down menu you will notice that the current rotation angle (in absolute terms) is displayed.

If you want to change the rotation angle of a smart object (without double-clicking it with the mouse and dragging a corner selection handle), you can type in a value in the Info Bar where the existing rotation angle is displayed.

ALSO TRY double-clicking an ellipse object in its center with the Ellipse Tool, a rectangle with the Rectangle Tool, or a QuickShape with the QuickShape Tool. The smart shape will change it's form (ie., ellipse to a rectangle, QuickShape to an ellipse, etc.).