Question

ABCD is the midpoint M of the diagonal BD of the parallelogram; BM is the value of angle AMB if bisects the angle ABC.​

Answer 1

Answer:

ABCD is a parallelogram in which M is the mid point of diagonal BD , BM bisect

the angle ABC. , therefore angle ABD = angle CBD = x°(let)……………..(1)

AD| | BC and BD is transversal ,

therefore angle ADB = angle CBD. (Alternate angles).

or. Angle ADB = x°…………………………..(2)

From eqn. (1) and (2)

Angle ABD = angle ADB. => side AB = side AD. , ( In ∆ ABD opposite angles are

equal , thus opposite sides are equal.)

∆ ABD is an isosceles triangle in which M is the mid point of base BD ,

angle AMB = angle AMD.

Thus , angle AMB =180°/2 = 90°