Question

In a quadrilateral ABCD, if AB || CD, ZD=2ZB, AD =b and CD = a, then the side AB is of length
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Answer 1

Hey mate

this question looks somewhat incomplete

is there any figure that you can upload with it?

Step-by-step explanation:

Hope you reply so I can help

thanks. :-)

Answer 2

Step-by-step explanation:

Given, AB∥CD, ∠D=2∠B, AD=b, CD=a

Now, AD=b    ∴CM=b

and CD=a      ∴AM=a

AB∥CD, thus, AMCD is a parallelogram.

∴∠D=∠AMC

∠AMC=2x

In △MCB

2x=∠MCB+∠x( ∵ Exterior angle is equal to sum of opposite interior angle)

=>∠MCB=x

=>∠MCB=∠B=x

∴MB=MC[As sides opposite to equal angles are equal]

Now, AB=AM+MB

   =>AB=a+b