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In the Given Figure, If Ab || Cd, Then the Value of X is - Mathematics

MCQ

In the given figure, if AB || CD, then the value of x is

Options

  • 20°

  • 30°

  • 45°

  • 60°

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Solution

Here AB || CD

Also, ∠1 and x are the two corresponding angles.

Then, according to the Corresponding Angles Axiom, which states:

If a transversal intersects two parallel lines, then each pair of corresponding angles are equal.

Therefore,

 ∠1  = x

Also, ∠1 and  (120° + x) form a linear pair, therefore, their sum must be supplementary.

Therefore,

 ∠1 + (120° + x) = 180°

On substituting ∠1 = x in equation above, we get: 

x + 120° + x = 180°

     2x + 120° = 180°

                 2x = 180° - 120° 

                 2x = 60°

                   `x = (60°)/2`

                    x = 30°

  Is there an error in this question or solution?
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APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 10 Lines and Angles
Q 11 | Page 53
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