Question

in the diagram, gh bisects ∠fgi.
a. solve for x and find m∠fgh.
b. find m∠hgi.
c. find m∠fgi.
a. x = (simplify your answer.)

Explanation:

Step1: Use angle - bisector property

Since $\overrightarrow{GH}$ bisects $\angle FGI$, then $m\angle FGH=m\angle HGI$. So, $2x - 9=3x-33$.

Step2: Solve the equation for x

Subtract $2x$ from both sides: $- 9=x - 33$. Then add 33 to both sides: $x=24$.

Step3: Find $m\angle FGH$

Substitute $x = 24$ into the expression for $m\angle FGH$: $m\angle FGH=2x - 9=2\times24-9=48 - 9 = 39^{\circ}$.

Step4: Find $m\angle HGI$

Since $m\angle HGI=m\angle FGH$, then $m\angle HGI = 39^{\circ}$.

Step5: Find $m\angle FGI$

$m\angle FGI=m\angle FGH + m\angle HGI=39^{\circ}+39^{\circ}=78^{\circ}$.

Answer:

a. $x = 24$, $m\angle FGH=39^{\circ}$
b. $m\angle HGI = 39^{\circ}$
c. $m\angle FGI=78^{\circ}$