Question

In the following figure, AB || CD and AD || BC. Now, find the value of b, c and d.

• A. b = 50°, c = 100° and d = 130°
• B. b = 130°, c = 50° and d = 130°
• C. b = 100°, c = 100° and d = 130°
• D. b = 50°, c = 130° and d = 50°

Answer 1

The correct option is B b = 130°, c = 50° and d = 130°


Given, AB || CD and AD || BC. Hence ABCD is a parallelogram.

$\angle$DAB = 50° (Given)
Then c = $\angle$ DAB = 50° (Opposite angles are equal)

If AD || BC, and AB is the transversal, then,
$\angle$ DAB + b = 180° (Co-interior angles)
$\Rightarrow$ 50° + b = 180°
$\Rightarrow$ b = 180° - 50° = 130°.
$\therefore$ b = 130°.

Now, b = d = 130° (Opposite angles are equal)

Then, b= 130°, c = 50°, d = 130°.