Question

if the diagonals of parallelogram ( jklm ) intersect at point ( n ), and ( kn = 3x + 7 ) while ( mn = 5x - 1 ), what mathematical principle allows you to set up an equation to solve for ( x )?
(1 point)
( x=square )

Explanation:

Step1: Use the property of parallelogram diagonals

In a parallelogram, the diagonals bisect each other. So \(KN = MN\).

Step2: Set up the equation

Given \(KN = 3x + 7\) and \(MN=5x - 1\), we set up the equation \(3x + 7=5x - 1\).

Step3: Solve the equation for \(x\)

Subtract \(3x\) from both sides: \(7 = 2x-1\).
Add \(1\) to both sides: \(8 = 2x\).
Divide both sides by \(2\): \(x = 4\).

Answer:

\(4\)