Question

If the angles A, B, C and D of a quadrilateral ABCD in the same order, are in the ratio $3:7:6:4$, then $\square ABCD$ is a

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

Answer 1

Answer: (C)

Trapezium

Let $\angle A=3x,\angle B=7x,\angle C=6x,\angle D=4x$

In a quadrilateral $\angle A+\angle B+\angle C+\angle D={360}^o$

$⟹3x+7x+6x+4x={360}^o$

$⟹20x={360}^o$

$\therefore x={18}^o$

$\therefore \angle A={54}^o,\angle B={126}^o,\angle C={108}^o,\angle D={72}^o$.

$\angle A+\angle B={180}^o$

$\angle C+\angle D={180}^o$

$\therefore AD\parallel BC$ ..... (pair of consecutive interior angles are supplementary)

Measure of all angles is different and $AD\parallel BC$

$\therefore ABCD$ is a trapezium.