Here's a trick. Use another prim as your pivot point. Here's how:
1. Start out with just one parasol section (PS), rotated so it's level. Rez another prim, and center it exactly at the PS's tip. The centering will be easy if you use the reference ruler. Simply select the PS, press shift-G (with chat closed) to reference it, and make sure Use Grid is turned on in the editor. Then you can easily snap the other prim into place via the on-screen rulers. Make sure to do it on all three axes. When you're done, set the ruler mode back to World. We have no further need for Reference mode at this time.
2. Link PS to the other prim. The PS should be the child in the linkset, not the parent.
3. Using the editor, not the on-screen manipulator, rotate the linkset on X or Y, to whatever roof pitch angle you plan on using. Judging by the very near success shown in your pictures, you should already know what this angle needs to be.
4. Unlink the two prims, and reset the base prim's rotation back to 0,0,0. Then re-link. Again, you want the PS to be the child, not the parent.
5. Now, duplicate the linkset by shift-dragging it any direction to leave a copy behind. Then press ctrl-Z to undo the movement of the original, returning it to the exact location of the copy. In the editor, rotate the original by 45 degrees on Z. The alignment between the two sections should now be perfect.
6. Repeat the duplicate-and-rotate procedure six more times, and your parasol will be complete.
7. Unlink everything, delete the extra prims, and link the parasol sections together.
So you know, the reason it was important to use the editor for the rotation, and not the on-screen manipulator, is that when you type in the numbers, the pivot point is the center of the parent prim. When you use the manipulator, the pivot point is always the geometric center of the entire linkset. By temporarily linking to a throw-away prim, and using the editor for rotation, you can effectively move the pivot anywhere you want. In this particular case, the pivot needed to be at the tip of the parasol section, since that's what in the end is the center of the whole parasol.
The entire above procedure should take about a minute or two to complete. Enjoy.
