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Question

In the given figure, if l1 || l2 and l3 || l4, what is y in terms of x?

(a) 90 + x

(b) 90 + 2x

(c) 90-x2

(d) 90 − 2x


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Solution

The given figure is:

Here, we have ∠2 and 2y are vertically opposite angles. Therefore,

...(i)

and x are alternate interior opposite angles.

Thus,

...(ii)

and are consecutive interior angles.

Theorem states: If a transversal intersects two parallel lines, then each pair of consecutive interior angles are supplementary.

Thus,

From (i) and (ii), we get:

Hence, the correct choice is (c).


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