In the parallelogram ABCD, the bisectors of ∠A and ∠B meet CD at the point E. The length of the side BC is 2 cm. Let us write the length of the side AB.

In the figure, In the parallelogram ABCD, the bisectors of ∠A and ∠B meet CD at the point E and BC = 2 cm

Now,

∠ABE = ∠CBE [BE is angle bisector of ∠B]

∠ABE = ∠BEC [Alternate interior angles]

⇒ ∠CBE = ∠BEC

⇒ BC = CE [Sides opposite to equal angles are equal] [1]

Similarly,

AD = DE

⇒ BC = DE [BC = AD, opposite sides of parallelogram are equal] [2]

Adding [1] and [2]

2BC = CE + DE

⇒ CD = 2BC

⇒ CD = 2(2) = 4 cm

Since, opposite sides of parallelogram are equal.

∴ AB = CD = 4 cm