A) x= 22, FGi=72
B)FGH=36
C) HGI=36
Explanation
when a ray bisects an angle, it means the angle is divided in two equal parts
then angle A( orange) is divided in two equal parts(yellow) by the ray B (blue)
Step 1
by the graph
[tex]\begin{gathered} 2x-8=\text{angle FGH} \\ 3x-30=\text{angle HGI} \\ \text{as we said before, } \\ \text{FGH}=\text{HGI} \\ \text{then} \\ 2x-8=3x-30 \end{gathered}[/tex]
Step 2
solve for x
[tex]\begin{gathered} 2x-8=3x-30 \\ 2x-3x=-30+8 \\ -x=-22 \\ x=22 \end{gathered}[/tex]
Step 3
replace the value of x to find the angles
[tex]\text{FGH}=2x-8=2(22)-8=44-8=36[/tex]
FGH=36
[tex]\begin{gathered} \text{HGI}=3x-30 \\ \text{HGI}=3(22)-30 \\ \text{HGI}=66-30 \\ \text{HGI}=36 \end{gathered}[/tex]
HGI=36
FGI=FGH+HGI
FGI=36+36
FGI=72
