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}`