Question

In a quadrilateral ABCD , if AB‖CD, what is the sum of∠A and ∠C?​

Answer 1

Answer:    :}

for example,

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

be happy :}