Question

example 2

1. in the figure, $overrightarrow{lf}$ and $overrightarrow{lk}$ are opposite rays. $overrightarrow{lg}$ bisects $angle flh$. if $mangle flg=(14x + 5)^{circ}$ and $mangle hlg=(17x - 1)^{circ}$, find $mangle flh$.

Explanation:

Step1: Use angle - bisector property

Since $\overrightarrow{LG}$ bisects $\angle FLH$, then $m\angle FLG=m\angle HLG$. So we set up the equation $14x + 5=17x-1$.

Step2: Solve the equation for $x$

Subtract $14x$ from both sides: $5 = 3x-1$. Then add 1 to both sides: $6=3x$. Divide both sides by 3, we get $x = 2$.

Step3: Find $m\angle FLG$ or $m\angle HLG$

Substitute $x = 2$ into $m\angle FLG=14x + 5$. Then $m\angle FLG=14\times2+5=28 + 5=33^{\circ}$.

Step4: Calculate $m\angle FLH$

Since $m\angle FLH=m\angle FLG + m\angle HLG$ and $m\angle FLG=m\angle HLG$, then $m\angle FLH=2m\angle FLG$. So $m\angle FLH=2\times33^{\circ}=66^{\circ}$.

Answer:

$66^{\circ}$