Explanation
We are required to show that the given quadrilateral below is a parallelogram:
This is achieved thus:
We know that one of the properties of a parallelogram is that its diagonals bisect each other. Therefore, we have:
[tex]\begin{gathered} |JN|=|NL| \\ 2x+2=4x-10 \\ \text{ Collect like terms} \\ 4x-2x=2+10 \\ 2x=12 \\ \frac{2x}{2}=\frac{12}{2} \\ x=6 \end{gathered}[/tex]Also, we have:
[tex]\begin{gathered} |MN|=|NK| \\ 6y+1=8y-6 \\ \text{ Collect like terms } \\ 8y-6y=1+6 \\ 2y=7 \\ \frac{2y}{2}=\frac{7}{2} \\ y=3.5 \end{gathered}[/tex]Hence, the quadrilateral is a parallelogram since the values of x and y corresponds to the given.
[tex]x=6;y=3.5[/tex]