Question

if: jk = 4x + 8, kl = 5x + 6, and jl = 86, find kl.

Explanation:

Step1: Apply segment - addition postulate

Since $JL = JK+KL$, we substitute the given expressions: $(4x + 8)+(5x + 6)=86$.

Step2: Combine like - terms

Combining the $x$ terms and the constant terms, we get $4x+5x + 8 + 6=86$, which simplifies to $9x+14 = 86$.

Step3: Solve for $x$

Subtract 14 from both sides: $9x=86 - 14$, so $9x=72$. Then divide both sides by 9: $x=\frac{72}{9}=8$.

Step4: Find $KL$

Substitute $x = 8$ into the expression for $KL$. Since $KL = 5x+6$, then $KL=5\times8 + 6$.
$KL=40 + 6=46$.

Answer:

$46$