Question

solve for x. (just put the number, not x = !!!!!) *
uc = 15
ec = x + 30

find vc. (just put the number!!!!!) *
vc = 3x - 12
cx = 12 + x
find vc

Explanation:

Step1: Use the property of parallelogram diagonals bisecting each other

In a parallelogram, the diagonals bisect each other. So \(UC=\frac{1}{2}EC\). Given \(UC = 15\) and \(EC=x + 30\), we have the equation \(15=\frac{1}{2}(x + 30)\).
Multiply both sides by \(2\): \(15\times2=x + 30\), which simplifies to \(30=x + 30\).
Subtract \(30\) from both sides: \(x=30 - 30=0\).

Step2: Use the property of diagonals bisecting each other for the second figure

Assuming the figure is a parallelogram (since diagonals bisect each other property is used), \(VC = CX\). Given \(VC=3x-12\) and \(CX = 12 + x\).
Set up the equation \(3x-12=12 + x\).
Subtract \(x\) from both sides: \(3x-x-12=12+x - x\), which gives \(2x-12=12\).
Add \(12\) to both sides: \(2x-12 + 12=12+12\), so \(2x=24\).
Divide both sides by \(2\): \(x = 12\).
Substitute \(x = 12\) into \(VC=3x-12\): \(VC=3\times12-12=36 - 12=24\).

Answer:

0
24