Question

1. find the value of x for which abcd must be a parallelogram.

4
19
18
5

Explanation:

Step1: Recall parallelogram property

In a parallelogram, opposite - sides are equal. So, if \(ABCD\) is a parallelogram, then \(BC = AD\).
We have \(BC=6 + 3x\) and \(AD=x + 14\).
Set up the equation \(6 + 3x=x + 14\).

Step2: Solve the equation for \(x\)

Subtract \(x\) from both sides of the equation:
\(6+3x - x=x + 14 - x\), which simplifies to \(6 + 2x=14\).
Then subtract 6 from both sides: \(6+2x - 6=14 - 6\), getting \(2x = 8\).
Divide both sides by 2: \(\frac{2x}{2}=\frac{8}{2}\), so \(x = 4\).

Answer:

4