The given figure represents a quadrilateral ABCD where AD = BC. What is the value of BC + CD?

∠CAD and ∠BCA are two equal angles (each equal to x) made by the transversal AC between the lines AD and BC.

These form alternate interior angles and are equal.

∴ AD || BC

Also, AD = BC (Given)

We know that a quadrilateral is a parallelogram if it has a pair of parallel and equal opposite sides.

Thus, ABCD is a parallelogram.

In a parallelogram, opposite sides are equal.

∴ BC = AD = 4 cm and CD = AB = 2 cm

Thus, BC + CD = 4 cm + 2 cm = 6 cm