Question

if: jk = 7x + 9, jl = 114, and kl = 9x + 9, find kl.

Explanation:

Step1: Use segment - addition postulate

Since $JL = JK+KL$, we substitute the given expressions: $114=(7x + 9)+(9x + 9)$.

Step2: Combine like - terms

$114 = 7x+9x + 9 + 9$, which simplifies to $114=16x + 18$.

Step3: Solve for $x$

Subtract 18 from both sides: $114−18 = 16x$, so $96 = 16x$. Then divide both sides by 16: $x=\frac{96}{16}=6$.

Step4: Find $KL$

Substitute $x = 6$ into the expression for $KL$. $KL=9x + 9$, so $KL=9\times6+9$.
$KL = 54 + 9=63$.

Answer:

63