Question

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

• A. Parallelogram
• B. Rectangle
• C. Trapezium
• D. Rhombus

Answer 1

Answer: (C)

Trapezium

Let A and D be 1x and 2x respectively.

Since its given that AB$\parallel$CD then,

$A+D={180}^{\circ }$ ..... (internal angles on same side of transversal)

$\Rightarrow x+2x={180}^{\circ }$

$\Rightarrow 3x={180}^{\circ }$

$\Rightarrow x={60}^{\circ }$

Therefore, $A={60}^{\circ }$, $D={120}^{\circ }$

Also,

Let C and B be 4y and 5y.

$C+B={180}^{\circ }$ ......... (interior angles on same side of transversal)

$\Rightarrow 4y+5y={180}^{\circ }$

$\Rightarrow 9y={180}^{\circ }$

$\Rightarrow y={20}^{\circ }$

Therefore, $C={80}^{\circ }$, $B={100}^{\circ }$.

The given quadrilateral ABCD is Trapezium.