Budapest: Math, then Math in the Synogogue

Yesterday we visited Budapest's "Great Synagogue" (here is a link to information about the synagogue) after a cool lecture on Graph Theory @ the BSM. After lunch with some of BSM's students, we walked over to the synagogue, and were completely blown away. And while the stained glass and mosaics were beautiful in their own right, it was hard not to look at them and see beautiful mathematics:






Just one question to get started: compute all the angles in each figure (with minimum possible assumptions about regularity, parallelism, etc.)