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In the Given Figure, If L1 || L2 and L3 || L4, What is Y in Terms of X? - Mathematics

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MCQ

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

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Solution

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`

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 17 | Page 54

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