Question

find ij in parallelogram ghij. the parallelogram ghij has side ij labeled 4z + 23 and side gh labeled 10z - 31. we need to find ij.

Explanation:

Step1: Set equal opposite sides

In a parallelogram, opposite sides are congruent, so $4z + 23 = 10z - 31$.

Step2: Solve for z

Rearrange to isolate z:
$23 + 31 = 10z - 4z$
$54 = 6z$
$z = \frac{54}{6} = 9$

Step3: Calculate IJ length

Substitute $z=9$ into $IJ = 4z + 23$:
$IJ = 4(9) + 23$

Answer:

$4(9)+23 = 36 + 23 = 59$
$IJ = 59$