Question

If ON = 5x – 4, LM = 4x + 7, NM = x – 7 and OL = 2y – 6, find the values of x and y for which LMNO must be a parallelogram. The diagram is not to scale. ...?

Answer 1

If LM=ON & LO=MN

LM=ON
 4x-7=5x-4
 -5x+4x=7-4
-x=3
x=-3

LO=MN
2y-6=x-7
2y-6=(-3)-7 ( I substituted the x by -3 )
2y-6=-10
2y=-10+6
2y=-4
y=-2

Therefore y=-2 and x=-3