Question

24. In the given figure if AB ∥ CD , then the value of x is

Answer 1

(C) 75
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Answer 2

Tip:

• Lines which are parallel to the same line are parallel to each other.

Explanation:

• We have the figure in which $AB|| CD$ .
• We have to find the value of $x$ .

• See the attachment for figure.

Step

Step 1 of 2:

We need to draw a line $PQ$ parallel to line $AB$ through the point $O$ as shown in the figure attached.

Now, $PQ||AB$ and $AB||CD$

Therefore, $PQ||CD$ (∵ Lines which are parallel to the same line are parallel to each other.)

Now, ∠$BXO$ $+$∠$XOQ$ $=180^o$  ( $PQ||AB$, Interior angles on the same sides of transversal $XO$)

But ∠$BXO$ $=140^o$

So, $140^o$ $+$∠$XOQ$ $=180^o$

∠$XOQ$ $=40^o$               -(1)

Step 2 of 2:

Now, ∠$QOY$ $=$ ∠$OYC$ ($PQ||CD$ , Alternate angles)

∠$QOY$$=35^o$                    -(2)

Adding (1) and (2)

∠$XOQ$ $+$∠$QOY$ $=40^o+35^o$

∠$XOY$ $=75^o$

Final Answer:

So, the value of $x$ is $75^o$

Hence the option C) is correct.