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

Option : (C)

Given, 

ABCD is a parallelogram,

M is mid point of BD 

BM bisects ∠B 

∵ ∠A+∠B = 180° 

[adjacent angles of parallelogram are supplementary]

In ∆AMB , 

∠AMB + \(\frac{1}{2}\)∠A + \(\frac{1}{2}\)∠B = 180°

= ∠AMB + \(\frac{1}{2}\)(∠A + ∠B) = 180°

=∠AMB + \(\frac{1}{2}\) x 180° = 180°

= ∠AMB = 180° - 90° = 90°