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In the Given Figure, If L1 || L2, What is the Value of Y? - Mathematics

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MCQ

In the given figure, if l1 || l2, 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 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°

Concept: Parallel Lines and a Transversal
  Is there an error in this question or solution?

APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 10 Lines and Angles
Q 16 | Page 54

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