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Question 22

In the given figure, $$ABCD$$ is a rectangle. The measure of angle $$x$$ is _______________ degrees.

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Correct Answer: 100

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Let us mark the points as shown in the figure asΒ $$E$$ , $$G$$Β and $$F$$

Now, line $$AB$$ is parallel to $$CD$$

So, $$\angle BEF+162=180$$Β°

$$\angle BEF=18$$Β°

And, $$\angle EFG=28$$Β°

Now, in triangle $$BEF$$

$$\angle EBF+\angle BFE+\angle FEB=180$$Β°

$$90+\angle BFE+18=180$$Β°

$$\angle BFE=72$$Β°

Now, Since lines $$AB$$ and $$BC$$ are parallel

So, $$x=\angle BFG$$

or, $$x=\angle BFE+\angle EFG$$

or, $$x=72+28=100$$Β°

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