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=(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=(40)/(2)\\\\\Rightarrow y=20.`

Thus, the required values are

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