Question

In a trapezium ABCD, the angles A,B,C and D are in the ratio 3 : 4 : 5 : 6 respectively.

Which of the following is true ?

• A. $AD\perp BC$
• B. $AD\parallel BC$
• C. $AB\parallel DC$
• D. $AB\perp DC$

Answer 1

The correct option is C

$AB\parallel DC$

Let the angles be $3x,4x,5x$ and $6x$.

$\because$ Sum of interior angles of a quadrilateral $={360}^{\circ }$

$\Rightarrow 3x+4x+5x+6x={360}^{\circ }$

$\Rightarrow 18x={360}^{\circ }$

$\Rightarrow x=\frac{{360}^{\circ }}{18}$

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

$\therefore Theanglesare$

$\angle A=3x=3\times 20={60}^{\circ }$

$\angle B=4x=4\times 20={80}^{\circ }$

$\angle C=5x=5\times 20={100}^{\circ }$

$\angle D=6x=6\times 20={120}^{\circ }$

$\therefore \angle A+\angle D={180}^{\circ }$ (Co-interior angles)

$\angle B+\angle C={180}^{\circ }$ (Co-interior angles)

$\therefore AB\parallel DC$