Answer:
[tex] \angle FGH = \angle FGI + \angle IGH \\ 82 = (6x + 10) + (5x - 5)[/tex]
collect like terms:
[tex]82 = (6x + 5x) + (10 - 5) \\ 82 = 11x + 5[/tex]
subtract 5 from both sides:
[tex]82 - 5 = (11x + 5) - 5 \\ 77 = 11x[/tex]
divide either sides by 11 [divide rule of equality]:
[tex] \frac{11x}{11} = \frac{77}{11} \\ \\ { \boxed{ \boxed{x = 7}}}[/tex]
