From the diagram, we know that:
[tex]OP\mleft\Vert NQ\mright?[/tex]
Then, using the proportionality theorem:
[tex]\frac{MN}{MO}=\frac{MQ}{MP}=\frac{NQ}{OP}[/tex]
Now, using the values of each segment:
[tex]\begin{gathered} \frac{8}{12}=\frac{10}{10+x} \\ 8(10+x)=12\cdot10 \\ 80+8x=120 \\ 8x=40 \\ \Rightarrow x=5 \\ \\ \frac{8}{12}=\frac{7}{y} \\ 8y=12\cdot7 \\ 8y=84 \\ \Rightarrow y=10.5 \end{gathered}[/tex]
