Questions: 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.)

Transcript text: In the diagram, $\overrightarrow{\mathrm{GH}}$ bisects $\angle \mathrm{FGI}$. a. Solve for $x$ and find $m \angle F G H$. b. Find $\mathrm{m} \angle \mathrm{HGI}$. c. Find $\mathrm{m} \angle \mathrm{FGI}$. a. $x=$ $\square$ (Simplify your answer.)

Solution

Solution Steps

Step 1: Set up the equation

Since $\overrightarrow{\mathrm{GH}}$ bisects $\angle \mathrm{FGI}$, we know that $\angle \mathrm{FGH}$ is congruent to $\angle \mathrm{HGI}$. Therefore, we can set up the equation: $3x - 3 = 4x - 14$

Step 2: Solve for x

Subtract $3x$ from both sides: $-3 = x - 14$ Add 14 to both sides: $11 = x$ So, $x = 11$.

Step 3: Find m∠FGH

Substitute $x = 11$ into the expression for m∠FGH: m∠FGH = $3x - 3$ m∠FGH = $3(11) - 3$ m∠FGH = $33 - 3$ m∠FGH = $30$

Step 4: Find m∠HGI

Since GH bisects ∠FGI, m∠HGI = m∠FGH. m∠HGI = $30$

Step 5: Find m∠FGI

m∠FGI = m∠FGH + m∠HGI m∠FGI = $30 + 30$ m∠FGI = $60$