Question

In the given figure, if l₁ || l₂, what is the value of y?

Options

• 100°

• 120°

• 135°

•  150°

Answer 1

Given figure is as follows:

It is given that l₁ || l₂.

∠1 and 3x are vertically opposite angles, which must be equal, that is,

 ∠1 = 3x (i)

Also,  ∠1and x are consecutive interior angles.

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

Thus,

∠1 + x = 180°

From equation (i), we get:

`3x + x = 180°`

        `4x = 180°`

          ` x = 180°/4`

           `x = 45°`

x and y form a linear pair. Therefore, their sum must be supplementary.

Thus,

 y + x =180°

Substituting, x = 45° in equation above, we get:

y + 45° = 180°

 y = 180° - 45°

 y = 135°