MCQ
If $\angle\text{A},\angle\text{B},\angle\text{C}$ and $\angle\text{D}$ of a quadrilateral $\text{ABCD}$ taken in order, are in the ratio $\{3 : 7 : 6 : 4\}$ then $\text{ABCD}$ is a:
- ARhombus.
- BKite.
- ✓Trapezium.
- DParallelogram.
✓
Answer
Correct option: C.
Trapezium.
Let the common multiple be $x$.
$\therefore$ The angle measure $3x, 7x, 6x$ and $4x$.
Since the sum of the angles of a quadrilateral is $360^\circ ,$ we have
$3x + 7x + 6x + 4x = 360$
$\Rightarrow 20x = 360$
$\Rightarrow x = 18^\circ$
$\therefore$ The angles of the quadrilateral are
$3x = 3(18) = 54^\circ$
$7x = 7(18) = 126^\circ$
$6x = 6(18) = 108^\circ$ and
$4x = 4(18) = 72^\circ$
Now $, 54 + 126 = 180^\circ$ and $108 + 72 = 180^\circ$
So, the angles are interior angles and hence we get one pair of parallel sides of $\text{ABCD}$.
Hence $, \text{ABCD}$ is a trapezium.
$\therefore$ The angle measure $3x, 7x, 6x$ and $4x$.
Since the sum of the angles of a quadrilateral is $360^\circ ,$ we have
$3x + 7x + 6x + 4x = 360$
$\Rightarrow 20x = 360$
$\Rightarrow x = 18^\circ$
$\therefore$ The angles of the quadrilateral are
$3x = 3(18) = 54^\circ$
$7x = 7(18) = 126^\circ$
$6x = 6(18) = 108^\circ$ and
$4x = 4(18) = 72^\circ$
Now $, 54 + 126 = 180^\circ$ and $108 + 72 = 180^\circ$
So, the angles are interior angles and hence we get one pair of parallel sides of $\text{ABCD}$.
Hence $, \text{ABCD}$ is a trapezium.
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