x = 3
Solution:
Given UVWX is a parallelogram.
UV, VW, XW, UX are sides of a parallelogram.
UW and XV are diagonals of a parallelogram.
VX = 14 and BX = x + 4
Property of parallelogram:
Diagonals of a parallelogram bisect each other.
⇒ VB = BX
⇒ VX = VB + BX
⇒ VX = BX + BX (since VB = BX)
⇒ VX = 2 BX
⇒ 14 = 2(x + 4)
⇒ 14 = 2x + 8
Subtract 8 from both sides of the equation, we get
⇒ 14 – 8 = 2x + 8 – 8
⇒ 6 = 2x
Divide by 2 on both sides of the equation, we get
⇒ 3 = x
⇒ x = 3
Hence the value of x is 3.