ABCD is a quadrilateral in which AB = 4 cm, CD= 6cm and the sum of A and 2D is 180°. What is the name of this quadrilateral?
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Step-by-step explanation:
Answer
a+b
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
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