Question

In the given figure, if AB || CD, then x = 

Options

• 100°

• 105°

• 110°

• 115°

Answer 1

100°

Explanation:

The given figure is as follows:

It is given that AB || CD.

Let us draw a line PQ parallel to AB and CD.

It is given that,

∠1 + ∠2 = 148°       ...(i)

Since, AB || PQ Thus, ∠APQ angle and ∠1 are consecutive interior angles.

Therefore,

∠1 + 132° = 180°

            ∠1 = 180° − 132°

            ∠1 = 48°          ...(ii)

Similarly, CD || PQ. Thus, x angle and ∠2 are corresponding angles.

Therefore,

∠2 = x        ...(iii)

On substituting (ii) and (iii) in (i):

48° + x = 148°

          x = 148° − 48°

          x = 100°