Question

if:

$kl = 2x + 2$,

$jl = 55$, and

$jk = 7x + 8$,

find $kl$.

Explanation:

Step1: Use segment - addition postulate

Since $JL=JK + KL$, we substitute the given expressions: $55=(7x + 8)+(2x + 2)$.

Step2: Combine like - terms

Combine the $x$ terms and the constant terms on the right - hand side: $55 = 7x+2x + 8 + 2$, which simplifies to $55=9x + 10$.

Step3: Solve for $x$

Subtract 10 from both sides of the equation: $55−10=9x$, so $45 = 9x$. Then divide both sides by 9: $x=\frac{45}{9}=5$.

Step4: Find $KL$

Substitute $x = 5$ into the expression for $KL$. Since $KL=2x + 2$, then $KL=2\times5+2$.
$KL=10 + 2=12$.

Answer:

12