Question

if $gj = 3c - 45$ and $ij = 5c - 89$, find the value of $c$ in parallelogram $fghi$.

Explanation:

Step1: Set segments equal (diag bisect)

In a parallelogram, diagonals bisect each other, so $GJ = IJ$.
$3c - 45 = 5c - 89$

Step2: Rearrange to isolate c terms

Subtract $3c$ from both sides.
$-45 = 2c - 89$

Step3: Isolate the 2c term

Add 89 to both sides.
$2c = 89 - 45$
$2c = 44$

Step4: Solve for c

Divide both sides by 2.
$c = \frac{44}{2}$

Answer:

$22$