Question

1. if $overline{lk}congoverline{mk}$, $lk = 7x - 10$, $kn=x + 3$, $mn = 9x - 11$, and $kj = 28$, find $lj$.

Explanation:

Step1: Set up equation from congruence

Since $\overline{LK}\cong\overline{MK}$, we have $7x - 10=x + 3$.

Step2: Solve for x

$7x-x=3 + 10$, $6x=13$, $x=\frac{13}{6}$.

Step3: Find LK

$LK=7x - 10=7\times\frac{13}{6}-10=\frac{91}{6}-10=\frac{91 - 60}{6}=\frac{31}{6}$.

Step4: Calculate LJ

$LJ=LK + KJ=\frac{31}{6}+28=\frac{31+168}{6}=\frac{199}{6}$.

Answer:

$\frac{199}{6}$