The line HG divides the line FI at point G. That means two angles have been formed which are, angle HGF and HGI.
Sum of angles on a straight line equals 180. If angle HGF and angle HGI both lie on the same line (FI), it means then, that;
HGF + HGI = 180
89 + HGI = 180
Subtract 89 from both sides of the equation and you have
HGI = 91
