last post, sorry to annoy those who are not interested...
You noticed that angles are rather narrow... (not so many degrees). In this case one can assume the three angles as independent each other and try to guess their values...
From the figure it is evident that 1+2+90 degrees must be 108, the internal angle of the pentangle, and the same for 3+90 ... then 3 = 1+2 = 18 degrees.
Furthermore if one start from a piece and construct the pentangle, considering just the 'twist' applied to the following piece, (angle 1), it can be concluded that 5 twist operations must give 90 because the last piece is rotated like that. Then the first guess is angle 1=18. Since in this case 1 and 3 (which are the wider) combine together more than the previous case, this estimate is the weakest.
Then, without any computer or math tool, one could infer that angle 3 = 18 degrees, angle 1 + angle 2 = 18 degrees as well and that angle 2 is much smaller than angle 1.
I would bet that if I used 15,3,18 or even 11,7,18 puzzle got assembled as well...
But, in that case, you had not spent so many kind words at me and .... that's why I chose the complicate way

PS kidding... but at the end, when things look a bit clearer, one often recognizes that there were shortcuts...
