Question

In the digram GH bisects FGI what is the answer for C.

Answer 1

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:

$3x-2=4x-13$

Now let us add 2 to both sides gives

$3x=4x-11$

subtracting 4x from both sides gives

$-x=-11$$x=11.$

Hence, x = 11.

The measure of FGH is

$3x-2=3(11)-2=31$

(B)

The measure of HGI is

$4x-13=4(11)-13=31$

(C)

The measure of FGI is the sum of HGI and FGH:

$\begin{gathered} \text{FGI}=\text{HGI}+\text{FGH}=31+31 \\ FGI=62^o \end{gathered}$