Question

1. find jl. jl = ____

Explanation:

Step1: Set up equation by equal - side property

Since $MN$ is a mid - segment and $JK = ML$, we can set up the equation $5r - 16=4r + 34$.
$5r-4r=34 + 16$

Step2: Solve for $r$

$r=50$

Step3: Find the length of $JL$

First, find the length of $ML = 4r+34$. Substitute $r = 50$ into $4r + 34$.
$ML=4\times50+34=200 + 34=234$
Since $JL=2ML$ (by the mid - segment theorem), $JL = 2\times234 = 468$

Answer:

$468$