The line GH bisects The triangle FGI meaning it divides it into two equal parts (that is the definition if bisection); therefore, the angles FGH and HGI are equal:
[tex]3x-2=4x-13[/tex]
Now let us add 2 to both sides gives
[tex]3x=4x-11[/tex]
subtracting 4x from both sides gives
[tex]-x=-11[/tex][tex]x=11.[/tex]
Hence, x = 11.
The measure of FGH is
[tex]3x-2=3(11)-2=31[/tex]
(B)
The measure of HGI is
[tex]4x-13=4(11)-13=31[/tex]
(C)
The measure of FGI is the sum of HGI and FGH:
[tex]\begin{gathered} \text{FGI}=\text{HGI}+\text{FGH}=31+31 \\ FGI=62^o \end{gathered}[/tex]
