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) $90-\frac{x}{2}$

(d) 90 − 2x

Answer 1

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).