Question

for what value of x must abcd be a parallelogram?
d c
12x - 5
a b
10x + 3
x = \square

Explanation:

Step1: Use the property of parallelogram

In a parallelogram, opposite sides are equal. So, \(DC = AB\).

Step2: Set up the equation

Given \(DC=12x - 5\) and \(AB = 10x+3\), we have the equation \(12x-5=10x + 3\).

Step3: Solve the equation

Subtract \(10x\) from both sides: \(12x-10x-5=10x - 10x+3\), which simplifies to \(2x-5 = 3\).
Add \(5\) to both sides: \(2x-5 + 5=3 + 5\), so \(2x=8\).
Divide both sides by \(2\): \(x=\frac{8}{2}=4\).

Answer:

\(x = 4\)