Answer: The required values are
u = 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
![u^\circ=140^\circ~~~~\textup{[alternate interior angles]}\\\\\Rightarrow u=140.](https://tex.z-dn.net/?f=u%5E%5Ccirc%3D140%5E%5Ccirc~~~~%5Ctextup%7B%5Balternate%20interior%20angles%5D%7D%5C%5C%5C%5C%5CRightarrow%20u%3D140.)
Now, we also have
![u^\circ=5v^\circ~~~~~\textup{[vertically opposite angles]}\\\\\Rightarrow u=5v\\\\\Rightarrow 140=5v\\\\\Rightarrow v=\dfrac{140}{5}\\\\\Rightarrow v=28.](https://tex.z-dn.net/?f=u%5E%5Ccirc%3D5v%5E%5Ccirc~~~~~%5Ctextup%7B%5Bvertically%20opposite%20angles%5D%7D%5C%5C%5C%5C%5CRightarrow%20u%3D5v%5C%5C%5C%5C%5CRightarrow%20140%3D5v%5C%5C%5C%5C%5CRightarrow%20v%3D%5Cdfrac%7B140%7D%7B5%7D%5C%5C%5C%5C%5CRightarrow%20v%3D28.)
Now, from the property of linear pair, we get

Since angles of measure w° and x° are alternate interior angles, so

Again, by using the property of linear pair, we get

Thus, the required values are
u = 140, v = 28, w = 40, x = 40 and y = 20.