Question

$overrightarrow{ej}$ bisects $angle def$, $mangle dej = 5x + 7$, $mangle jef = 8x - 8$. find x.

Explanation:

Step1: Use angle - bisector property

Since $\overrightarrow{EJ}$ bisects $\angle DEF$, then $m\angle DEJ=m\angle JEF$. So, $5x + 7=8x - 8$.

Step2: Rearrange the equation

Subtract $5x$ from both sides: $7 = 8x-5x - 8$, which simplifies to $7 = 3x-8$.

Step3: Solve for $x$

Add 8 to both sides: $7 + 8=3x$, so $15 = 3x$. Then divide both sides by 3: $x=\frac{15}{3}=5$.

Answer:

$x = 5$