I guess this is 3D drawing coz according to physics opposite anglesshould be same. So according to the prism Y should be equal to Z and hence siny/sinz should be equal to one. But it it is not ,according to the data you gave. I guess this needs some higher physics analyst
I think it's just a sketch and not detailed, I have dealt with thousands of incorrect sketches even on the highest level of my physics studies Sometimes Profs or their assistants are just too lazy to not only put some new numbers there every year but also to redraw the sketches
Oh and siny/sinz doesn't need to be 1 necessarily! Only when light travels in vacuum! If the prism is denser (which it is of course) n>0 ! n=1.58 suggests that the prism might be made out of Polycarbonate
Since opposite angles must be same Y must be equal to 45+z(look carefully on that deviated angle) Now I guess in that internal triangle,which you mentioned 90 degrees and if it is correct, the other angles must be 45 and 45 and that implies x must be 45. I guess am not correct 100% but have a look on this solution!