Here is another method to make the same without using any angles :-)
Inspired from the model How to model a Dodecahedron from scratch by Steen Winther.
Here is the model:
Hope this will be helpful to many..
First, make a simple pentagon and make a planer surface from it.
Save the file with any name, Say "Surface".
Now Make an Assembly and import that part "surface".
Insert another same surface and make co-incident relations(mates) of
As shown in the picture.
Insert 3rd surface and again make relations(mates) like the previous one.
but with another edge of the base surface as shown in the picture.
Now make an edge-to-edge mate with one edge of the second part and second edge of the third part as shown in the pictures.
Add another part and make two edge-to-edge mates as shown in the picture.
Then insert more surfaces and add all the required mates,
i have shown the last mate required in the assembly.
Click "Save as".
Select "Part" as type to save the file with any name say "Final".
Remember to check "exterior Faces" in "Geometry to save".
Now open the saved part file and knit all the surfaces to make the part a solid.
Remember to Check "Try to make solid" under selections.
Additionally we can add fillets to the model.
Best way to add fillets is to use FilletExpert.
Here is a cascade view of all the files.(Surface, Assembly and Final).