Question

determine the value of x that would make quadrilateral lmno a parallelogram.
3
9
11
18

Explanation:

Step1: Recall parallelogram property

In a parallelogram, the diagonals bisect each other. So, \(LP = PN\) and \(MP=PO\). Here we use \(LP = PN\), so \(x + 2=2x - 7\).

Step2: Solve the equation for x

Subtract \(x\) from both sides: \(x+2 - x=2x - 7 - x\), which gives \(2=x - 7\).

Step3: Isolate x

Add 7 to both sides: \(2 + 7=x-7 + 7\), so \(x = 9\).

Answer:

9