Answer: The required values areu = 140, v = 28, w = 40, x = 40 and y = 20.Step-by-step explanation: We are given to find the values of u, v, w, x and y from the figure shown.We see that the lines AB and CD are parallel to each other and PS is a transversal.So, we must have[tex]u^\circ=140^\circ~~~~\textup{[alternate interior angles]}\\\\\Rightarrow u=140.[/tex]Now, we also have[tex]u^\circ=5v^\circ~~~~~\textup{[vertically opposite angles]}\\\\\Rightarrow u=5v\\\\\Rightarrow 140=5v\\\\\Rightarrow v=\dfrac{140}{5}\\\\\Rightarrow v=28.[/tex]Now, from the property of linear pair, we get[tex]u^\circ+x^\circ=180^\circ\\\\\Rightarrow u+x=180\\\\\rightarrow 140+x=180\\\\\Rightarrow x=180-140\\\\\Rightarrow x=40.[/tex]Since angles of measure w° and x° are alternate interior angles, so[tex]w^\circ=x^\circ=40^\circ\\\\\Rightarrow w=40.[/tex]Again, by using the property of linear pair, we get[tex]2y^\circ+140^\circ=180^\circ\\\\\Rightarrow 2y+140=180\\\\\Rightarrow 2y=40\\\\\Rightarrow y=\dfrac{40}{2}\\\\\Rightarrow y=20.[/tex]Thus, the required values areu = 140, v = 28, w = 40, x = 40 and y = 20.