We have a parallelogram.
The diagonals of a parallelogram bisect each other. This means that each diagonal is divided in two equal segments by the other diagonal.
This let us write:
[tex]9=2n-1[/tex]
and
[tex]m+8=3m[/tex]
We can solve for n as:
[tex]\begin{gathered} 9=2n-1 \\ 9+1=2n \\ 10=2n \\ n=\frac{10}{2} \\ n=5 \end{gathered}[/tex]
and for m as:
[tex]\begin{gathered} m+8=3m \\ m-3m=-8 \\ -2m=-8 \\ m=\frac{-8}{-2} \\ m=4 \end{gathered}[/tex]
Answer: the value of m is 4.
