Question

The measures of the angles of the quadrilateral ABCD are in the ratio $2:3:4:1$. Determine the type of the quadrilateral.

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

Answer 1

The correct option is A Trapezium

Let the angles of the quadrilateral in degrees be $=2a,3a,4a$ and $a$
Since the sum of angles of a quadrilateral $={360}^o$,

$2a+3a+4a+a={360}^o$

$10a={360}^o$
$a=36$

So,
the angles of the quadrilateral are $=2a={72}^o,3a={108}^o,4a={144}^o$ and
$a=36$
Suppose
$\angle A={72}^o$ and $\angle B={108}^o$
Sum of $\angle A$ and $\angle B={72}^o+{108}^o={180}^o$
This means, AB is a transversal to the parallel sides $AD$ and $BC$ as the sum of
interior angles on the same side of transversal is ${180}^o$
Hence, $AD\parallel BC$ and $ABCD$ is a trapezium.