Since they are opposite angles about the intersection of two straight lines they are equal angles....
5x+12=6x-10 subtract 12 from both sides
5x=6x-22 subtract 6x from both sides
-x=-22 divide both sides by -1
x=22°
So those angles are 5*22+12=122°
Now HJI is an adjacent angle so it is 180°-122°=58°