Question

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

विकल्प

• 20°

• 30°

• 45°

• 60°

Answer 1

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°