Given that,
[tex]\bar{PQ}\cong\bar{\bar{MN}}(S\text{ince both are straight lines)}[/tex]
Solving for angle x
[tex]\angle x+86^0=180^0(s\text{um of angles on a straight line)}[/tex]
Subtract 86° from both sides
[tex]\begin{gathered} \angle x+86^0-86^0=180^0-86^0 \\ \angle x+0=94^0 \\ \angle x=94^0 \end{gathered}[/tex]
Solving for angle y
[tex]\angle y+30^0+86^0=180^0(s\text{um of angles on a straight line)}[/tex][tex]\angle y+116^0=180^0[/tex]
Subtract 116° from both sides
[tex]\begin{gathered} \angle y+116^0-116^0=180^0-116^0 \\ \angle y+0=64^0 \\ \angle y=64^0 \end{gathered}[/tex]
Therefore,
[tex]\begin{gathered} m\angle x+m\angle y=\angle x+\angle y=94^0+64^0 \\ m\angle x+m\angle y=158^0 \\ \therefore m\angle x+m\angle y=158^0 \end{gathered}[/tex]
The answer is
[tex]m\angle x+m\angle y=158^0[/tex]
