As the line segment GH bisects the angle FGI, we have two equal angles, angle FGH and angle IGH. Therefore, we have,
[tex]\begin{gathered} 4x-6=5x-13 \\ 5x-4x=13-6 \\ x=7 \end{gathered}[/tex]
Thus, we have x = 7. Now,
[tex]\begin{gathered} <\text{HGI}=5\times7-13=35-13=22 \\ <\text{FGH}=4\times7-6=28-6=22 \\ <\text{FGI = 22+22=44} \end{gathered}[/tex]
Thus, x = 7, < FGH = 22,
