From the given image we have,
[tex]\begin{gathered} \angle BCX=40^{\circ} \\ \angle ABC=40^{\circ} \end{gathered}[/tex]
Therefore, angle GCF is which is opposite to angle BCX
[tex]\angle GCF=40^{\circ}[/tex]
Now,
[tex]\angle ABC+\angle EBL+\angle CBX=180^{\circ}[/tex][tex]\begin{gathered} 40\text{ + 90 + }\angle CBX=180^{\circ} \\ \angle CBX=180-130 \\ \angle CBX=50^{\circ} \end{gathered}[/tex][tex]Now,\angle BXC=\angle LBX[/tex][tex]\angle BXC=90^{\circ}[/tex]
