Question

question 4 angles and congruence - practice 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 \( \angle FLH \), we have \( m\angle FLG = m\angle HLG \).
So, \( 14x + 5 = 17x - 1 \).

Step2: Solve for \( x \)

Subtract \( 14x \) from both sides: \( 5 = 3x - 1 \).
Add 1 to both sides: \( 6 = 3x \).
Divide by 3: \( x = 2 \).

Step3: Find \( m\angle FLG \)

Substitute \( x = 2 \) into \( m\angle FLG = (14x + 5)^\circ \):
\( m\angle FLG = 14(2) + 5 = 28 + 5 = 33^\circ \).

Step4: Find \( m\angle FLH \)

Since \( \overrightarrow{LG} \) bisects \( \angle FLH \), \( m\angle FLH = 2 \times m\angle FLG \).
So, \( m\angle FLH = 2 \times 33^\circ = 66^\circ \).

Answer:

\( 66^\circ \)