In the parallelogram ABCD, M is the mid-point of the diagonal BD; if BM bisects ∠ABC, then the value of ∠AMB is

As, BM is angle bisector of ∠ABC

∠ABD = ∠CBD

Also, ∠ADB = ∠CBD [Alternate interior angles]

⇒ ∠ABD = ∠CBD

⇒ AB = AD [Opposite sides to equal sides are equal]

Also, if adjacent sides of a parallelogram are equal then it’s a rhombus

Therefore, ABCD is a rhombus,

Also, Diagonals of a rhombus intersect each other at right angle

⇒ ∠BMC = 90°