Question

in the figure, $overrightarrow{gk}$ bisects $angle fgh$. if $mangle fgk = 3v - 4$ and $mangle kgh = 2v+7$, find $x$.
o 58
o 11
o 33
o 29

Explanation:

Step1: Use angle - bisector property

Since $\overrightarrow{GK}$ bisects $\angle FGH$, then $m\angle FGK=m\angle KGH$. So, $3v - 4=2v + 7$.

Step2: Solve for $v$

Subtract $2v$ from both sides of the equation: $3v-2v - 4=2v-2v + 7$, which simplifies to $v-4 = 7$. Then add 4 to both sides: $v=7 + 4=11$.

Step3: Find $m\angle FGK$

Substitute $v = 11$ into the expression for $m\angle FGK$: $m\angle FGK=3v - 4=3\times11-4=33 - 4=29$.

Step4: Find $x$

Since $x=m\angle FGK$, then $x = 29$.

Answer:

29