Question

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 congruent segments

Since $\overline{LK}\cong\overline{MK}$, and $LK = 7x - 10$, and $MK=MN - KN$, with $MN = 9x - 11$ and $KN=x + 3$. Then $MK=(9x - 11)-(x + 3)=9x-11 - x - 3=8x-14$. Set $7x - 10=8x - 14$.
$7x-10=8x - 14$

Step2: Solve for x

Subtract $7x$ from both sides: $-10=x - 14$. Then add 14 to both sides.
$-10+14=x$, so $x = 4$.

Step3: Find LK

Substitute $x = 4$ into the expression for $LK$. $LK=7x - 10=7\times4-10=28 - 10=18$.

Step4: Find LJ

Since $LJ=LK + KJ$, and $KJ = 28$, $LK = 18$. Then $LJ=18+28=46$.

Answer:

46