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Question

In quadrilateral ABCD, side AB is parallel to side DC. If A:D=1:2 and C:B=4:5. Assign a special name to quadrilateral ABCD.

A
Parallelogram
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B
Rectangle
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C
Trapezium
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D
Rhombus
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Solution

The correct option is B Trapezium

Let A and D be 1x and 2x respectively.
Since its given that ABCD then,
A+D=180 ..... (internal angles on same side of transversal)
x+2x=180
3x=180
x=60
Therefore, A=60, D=120
Also,
Let C and B be 4y and 5y.
C+B=180 ......... (interior angles on same side of transversal)
4y+5y=180
9y=180
y=20
Therefore, C=80, B=100.
The given quadrilateral ABCD is Trapezium.

811428_179878_ans_4d59dfaf6d8b4d28b9480962d9902c92.png

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