Question

If the angles of a quadrilateral ABCD, taken in order, are in the ratio, $3:7:6:4$, then ABCD is a :

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

Answer 1

The correct option is D trapezium

Given ratio of angles of quadrilateral ABCD is $3:7:6:4$

Let the angles of quadrilateral ABCD be $3x,7x,6x,4x$ respectively.

We know that the sum of all amgles is $360°$

$\therefore x=18°$

i.e, $\angle A=3x=54°$ $\angle C=6x=108°$

$\angle B=7x=126°$ $\angle D=4x=72°$

$\Rightarrow \angle BCE=\angle ADC=72°$

Since the corresponding angles are equal,

$BC\parallel AD$

$\therefore$ Sum of interior angles

$\Rightarrow \angle A+\angle B=126°+54°=180°$

$\Rightarrow \angle C+\angle D=108°+72°=180°$

$\therefore$ ABCD is a trapezium.

Hence, the answer is trapezium.