If , , and of a quadrilateral ABCD taken in order, are in the rat… - Vidyadip

MCQ

If $\angle\text{A},\angle\text{B},\angle\text{C}$ and $\angle\text{D}$ of a quadrilateral $ABCD$ taken in order, are in the ratio $3 : 7 : 6 : 4$ then $ABCD$ is a:

A
Rhombus.
B
Kite.
✓
Trapezium.
D
Parallelogram.

✓

Answer

Correct option: C.

Trapezium.

Let the common multiple be $x .$
$\therefore$ The angle measure $3 x, 7 x, 6 x$ and $4 x$.
Since the sum of the angles of a quadrilateral is $360^{\circ}$, we have
$3x + 7x + 6x + 4x = 360$
$⇒ 20x = 360$
$⇒ x = 18°$
$\therefore$ The angles of the quadrilateral are
$3x = 3(18) = 54°$
$7x = 7(18) = 126°$
$6x = 6(18) = 108°$ and
$4x = 4(18) = 72°$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 $A B C D$. Hence, $A B C D$ is a trapezium.

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