Question

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

Explanation:

Step1: Use the property of congruent segments

Since $\overline{LK}\cong\overline{MK}$, we have $LK = MK$. Given $LK=7x - 10$ and $MK = 9x-11 - (x + 3)$. First, simplify the expression for $MK$: $MK=9x-11 - x - 3=8x-14$. Then set up the equation $7x - 10=8x - 14$.

Step2: Solve the equation for x

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

Step3: Find the length of LK

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

Step4: Find the length of LJ

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

Answer:

46