Question

If the angles $A,B,C,D$ of a quadrilateral , taken in order are in the ratio $7:13:12:8$, then $ABCD$ is:

• A. rhombus
• B. parallelogram
• C. trapezium
• D. kite

Answer 1

Answer: (C)

trapezium

Let the angles be $7x,13x,12x$ and $8x$
Then, $7x+13x+12x+8x={360}^o$
$\Rightarrow$ $40x={360}^o$ $\Rightarrow$ $x=9^o$
$\therefore$ $40x={360}^o$
$\therefore$ The angles taken in order are ${63}^o,{117}^o,{108}^o,{72}^o$
This shows that tow pairs of adjacent angles are supplementary $({63}^o+{117}^o={108}^o$ and ${108}^o+{72}^o={180}^o$), but opposite angles are not equal.
Therefore, the given quadrilateral will be a trapezium.