Question

algebra in the figure, $overrightarrow{kj}$ and $overrightarrow{km}$ are opposite rays, and $overrightarrow{kn}$ bisects $angle{jkl}$. if $mangle{jkn}=8x - 13$ and $mangle{nkl}=6x + 11$, find $mangle{jkn}$.

Explanation:

Step1: Use angle - bisector property

Since $\overrightarrow{KN}$ bisects $\angle{JKL}$, then $m\angle{JKN}=m\angle{NKL}$.
So, $8x - 13=6x + 11$.

Step2: Solve the equation for $x$

Subtract $6x$ from both sides: $8x-6x - 13=6x-6x + 11$, which simplifies to $2x-13 = 11$.
Add 13 to both sides: $2x-13 + 13=11 + 13$, so $2x=24$.
Divide both sides by 2: $x = 12$.

Step3: Find $m\angle{JKN}$

Substitute $x = 12$ into the expression for $m\angle{JKN}$: $m\angle{JKN}=8x-13$.
$m\angle{JKN}=8\times12-13=96 - 13=83$.

Answer:

$83$