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MCQ

In the given figure, if l_{1} || l_{2}, what is the value of y?

#### Options

100°

120°

135°

150°

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#### Solution

Given figure is as follows:

It is given that l_{1} || l_{2}.

∠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°

Concept: Parallel Lines and a Transversal

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