Applying linear pair property on the line DG,
[tex]\begin{gathered} 8x+7+59^{\circ}+12x-6=180^{\circ} \\ \Rightarrow20x+60=180 \\ \Rightarrow20x=120 \\ \Rightarrow x=6 \end{gathered}[/tex]
The measure of angle GIF can be determined as,
[tex]\begin{gathered} \angle GIF=12x-6 \\ =12\times6-6 \\ =72-6 \\ =66^{\circ} \end{gathered}[/tex]
Thus, the required value of x is 6 and angle GIF is 66 degress.
