Question

How do I find if it does work. If it does explain or if It doesn’t

Answer 1

Yes, J can be determined if H=54. The interior angles of a triangle always add up to 180. Since we know H=54 and J and I are equal.
J+I+H=180
J+I+54=180
J+I= 126
Because J&I are equal you can just divide 126 by 2
J=126/2
J= 63