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 congruent segments

Since $\overline{LK}\cong\overline{MK}$, we have $LK = MK$. Given $LK = 7x - 10$ and $MK=MN - KN$. Also, $KN=x + 3$ and $MN=9x - 11$. So $MK=(9x - 11)-(x + 3)=9x-11 - x - 3=8x-14$. Then set $7x - 10=8x - 14$.

Step2: Solve for $x$

Subtract $7x$ from both sides of $7x - 10=8x - 14$: $- 10=x - 14$. Add 14 to both sides, we get $x = 4$.

Step3: Find the length of $LK$

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

Step4: Find the length of $LJ$

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

Answer:

$46$