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Question
ABCD is a parallelogram, M is the mid-point of BD and BM bisects ∠B. Then ∠AMB =
Options
45°
60°
90°
75°
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Solution
Figure is given as follows:
ABCD is a parallelogram.
It is given that :
BM bisects ∠B
Therefore,
∠1 = ∠2
But,
∠2 = ∠3 (Alternate interior opposite angles asDC || AB )
Therefore,
∠1 = ∠3
In ΔABD,
∠1 =∠3
Sides opposite to equal angles are equal.
Thus,
AD = AB
Also,
CD = AB (Opposite sides of a parallelogram are equal)
Thus,
CD = AD
ABCD is a parallelogram with AD = AB
Therefore,
ABCD is a rhombus.
And we know that diagonals of the rhombus bisect each other at right angle.
Thus, ∠AMB = 90°
Hence the correct choice is (c).
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