Question

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

Options

•  90 + x

•  90 + 2x

•  `90 + x/2`

• 90 − 2x

Answer 1

The given figure is:

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

 ∠2 = 2y  ...(i)

∠1 and x are alternate interior opposite angles.

Thus,

 ∠1 = x     ...(ii)

∠1 and ∠2 are consecutive interior angles.

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

Thus,

∠1 + ∠2 180° 

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

x +2y = 180°

2y = 180° - x

`y = (180° -x)/2`

`y = (180°)/2 - x /2`

 `y = 90° - x /2`