Question

ABCD is a parallelogram, M is the mid-point of BD and BM bisects ∠B. Then ∠AMB =

(a) 45°

(b) 60°

(c) 90°

(d) 75°

Answer 1

Figure is given as follows:

ABCD is a parallelogram.

It is given that :

BM bisects

Therefore,

But,

(Alternate interior opposite angles as)

Therefore,

In,

Sides opposite to equal angles are equal.

Thus,

Also,

(Opposite sides of a parallelogram are equal)

Thus,

ABCD is a parallelogram with

Therefore,

ABCD is a rhombus.

And we know that diagonals of the rhombus bisect each other at right angle.

Thus,

Hence the correct choice is (c).