Question

In the diagram, GH bisects ∠FGI.Solve for x and find m∠FGH.a. X=b. Find m∠HGI.C. Find m∠FGI.(Simplify your answer.)

Answer 1

(a)19 degrees

(b)29 degrees

(c)58 degrees

Step-by-step explanation:

If GH bisects ∠FGI, it means it divides it into two equal parts ∠FGH and ∠HGI.

`\begin{gathered} m\angle FGH=m\angle\text{HGI} \\ (2x-9)^0=(3x-28)^0 \end{gathered}`

(a)We solve the equation above for x.

`\begin{gathered} 3x-2x=-9+28 \\ x=19 \end{gathered}`

(b)

`\begin{gathered} m\angle HGI=3x-28 \\ =3(19)-28 \\ =57-28 \\ =29^0 \end{gathered}`

(c)

`\begin{gathered} m\angle FGI=2* m\angle HGI \\ =2*29^0 \\ =58^0 \end{gathered}`