The Eightfold Path

The angle α is 22,5°. 

First look at isosceles triangles GED and GCD. It is a matter of angle chasing to show that angle CGE is 45°.
Now triangle GBC is also isosceles, because Thales implies its top corner is 90°. Therefore BC=GC. It also implies that 180-2β=135 and therefore β=22,5°.
Next, using SAS, one can show that triangles GCD and BCF are congruent. Since triangle BCF is now isosceles, we have 45-α=β and hence α=22,5°.

 6) Math Art

Math Art sent by Rafael Araujo