Opposite angles have the same measure. So, we can set the following equation:
[tex] 2x+2=3x-52 [/tex]
From here, we can forget about the geometry and continue algebraically: subtract 2x from both sides:
[tex] 2 = x-52 [/tex]
Add 52 to both sides:
[tex] 57=x\iff x=57 [/tex]
