Focus on the triangle. One angle measures 31+x, the bottom right measures 45 (it is supplementary to a 135 angle). The bottom left measures x+12 because it is opposite to the x+12 angle. The sum of interior angles of a triangle must be 180, so we have
[tex](31+x)+45+(x+12)=180 \iff 2x+88=180 \iff 2x=92 \iff x=46[/tex]
Angle y is supplementary with the x+12 angle, so we have
[tex]y=180-(x+12)=180-x-12=180-46-12=122[/tex]
Finally, angle x+12 measures 46+12=58
