Question

1. $overrightarrow{yl}$ is the angle bisector of $angle jyf$. find the value of $x$ if $mangle1 = 8x + 10$ and $mangle2 = 11x - 8$.

Explanation:

Step1: Set angles equal (angle bisector)

Since $\overrightarrow{YL}$ bisects $\angle JYF$, $m\angle 1 = m\angle 2$.
$$8x + 10 = 11x - 8$$

Step2: Isolate x terms

Subtract $8x$ from both sides.
$$10 = 3x - 8$$

Step3: Isolate constant terms

Add 8 to both sides.
$$18 = 3x$$

Step4: Solve for x

Divide by 3.
$$x = \frac{18}{3} = 6$$

Answer:

$x=6$