Question

In the diagram, ray GH bisects angle FGI. A. Solve for x and find m angle FGH.B. Find m angle HGI.C. Find m angle FGI.

Answer 1

A) x= 22, FGi=72

B)FGH=36

C) HGI=36

Step-by-step 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

`\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}`

Step 2

solve for x

`\begin{gathered} 2x-8=3x-30 \\ 2x-3x=-30+8 \\ -x=-22 \\ x=22 \end{gathered}`

Step 3

replace the value of x to find the angles

`\text{FGH}=2x-8=2(22)-8=44-8=36`

FGH=36

`\begin{gathered} \text{HGI}=3x-30 \\ \text{HGI}=3(22)-30 \\ \text{HGI}=66-30 \\ \text{HGI}=36 \end{gathered}`

HGI=36

FGI=FGH+HGI

FGI=36+36

FGI=72