Answer :
Since RSTU and MNOP are similar, we get that:
[tex]\begin{gathered} \frac{UR}{PM}=\frac{RS}{MN}, \\ m\angle S=m\angle N. \end{gathered}[/tex]Substituting UR=5x, RS=14, MN=10, and PM=15 we get:
[tex]\frac{5x}{15}=\frac{14}{10}\text{.}[/tex]Simplifying the above result we get:
[tex]\frac{x}{3}=\frac{7}{5}\text{.}[/tex]Multiplying the above result by 3 we get:
[tex]\begin{gathered} \frac{x}{3}\times3=\frac{7}{5}\times3, \\ x=\frac{21}{5}\text{.} \end{gathered}[/tex]Now, from the given diagram we get that:
[tex]\begin{gathered} m\angle M=m\angle D, \\ m\angle P=m\angle N. \end{gathered}[/tex]Therefore:
[tex]m\angle M+m\angle N=180^{\circ}\text{.}[/tex]Then:
[tex]m\angle M+m\angle S=180^{\circ}.[/tex]Substituting m∠M= y degrees and m∠S=50 degrees we get:
[tex]y^{\circ}+50^{\circ}=180^{\circ}.[/tex]Subtracting 50 degrees from the above equation we get:
[tex]\begin{gathered} y^{\circ}+50^{\circ}-50^{\circ}=180^{\circ}-50^{\circ}, \\ y^{\circ}=130^{\circ}, \\ y=130. \end{gathered}[/tex]Answer:
[tex]\begin{gathered} x=\frac{21}{5}, \\ y=130. \end{gathered}[/tex]