Question

What is the value of u, v, w, x, and y?

Answer 1

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

$u^\circ=140^\circ~~~~\textup{[alternate interior angles]}\\\\\Rightarrow u=140.$

Now, we also have

$u^\circ=5v^\circ~~~~~\textup{[vertically opposite angles]}\\\\\Rightarrow u=5v\\\\\Rightarrow 140=5v\\\\\Rightarrow v=\dfrac{140}{5}\\\\\Rightarrow v=28.$

Now, from the property of linear pair, we get

$u^\circ+x^\circ=180^\circ\\\\\Rightarrow u+x=180\\\\\rightarrow 140+x=180\\\\\Rightarrow x=180-140\\\\\Rightarrow x=40.$

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

$w^\circ=x^\circ=40^\circ\\\\\Rightarrow w=40.$

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

$2y^\circ+140^\circ=180^\circ\\\\\Rightarrow 2y+140=180\\\\\Rightarrow 2y=40\\\\\Rightarrow y=\dfrac{40}{2}\\\\\Rightarrow y=20.$

Thus, the required values are

u = 140, v = 28, w = 40, x = 40 and y = 20.

Answer 2

U is 140 degrees. X is 40 degrees. W is 40. V is 28. And, y is 80.

Sorry if I'm wrong.