Question

what must each length be in order for quadrilateral jklm to be a parallelogram?
jk: 3x - 2, lm: x + 6, jm: 2x - 1

1. jk
2. jl

Explanation:

Step1: Set opposite sides equal

In a parallelogram, opposite sides are congruent, so $JK = LM$.
$3x - 2 = x + 6$

Step2: Solve for $x$

Subtract $x$ from both sides, then add 2 to both sides.
$3x - x = 6 + 2$
$2x = 8$
$x = 4$

Step3: Calculate length of $JK$

Substitute $x=4$ into $JK=3x-2$.
$JK = 3(4) - 2 = 12 - 2$

Step4: Calculate length of $JL$

First, note that the diagonals of a parallelogram bisect each other, so the full diagonal $JL = 2\times(2x-1)$. Substitute $x=4$.
$JL = 2(2(4)-1) = 2(8-1) = 2\times7$

Answer:

1. $JK = 10$
2. $JL = 14$