Question

The measure of the angles of a quadrilateral ABCD are respectively in the ratio 1 : 2 : 3 : 4. What type of quadrilateral is ABCD?

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

Answer 1

The correct option is A Trapezium

Let the ratio of angles be '$x$'.
$\therefore \angle A=x,\angle B=2x,\angle C=3x,\angle D=4x$
$x+2x+3x+4x={360}^{\circ }$
$10x={360}^{\circ }$
$x={36}^{\circ }$
$\therefore \angle A={36}^{\circ },\angle B={72}^{\circ },$
$\angle C={108}^{\circ },\angle D={144}^{\circ }$
Now we see that
$\angle A+\angle D={180}^{\circ }and\angle B+\angle C={180}^{\circ }$
$⟹AB\parallel DC$

But $\angle A\ne \angle C$
So $ABCD$ is not a parallelogram.
$\because$ One pair of opposite sides in ABCD are parallel.
$\therefore$ ABCD is a trapezium