Question

In quadrilateral ABCD

$\angle A:\angle B:\angle C:\angle D=3:4:5:6$

then quadrilateral ABCD is a

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

Answer 1

The correct option is D

Trapezium

$\angle A:\angle B:\angle C:\angle D=3:4:5:6\left(given\right)$

Let

$\angle A=3x^{\circ }$

$\angle B=4x^{\circ }$

$\angle C=5x^{\circ }$

$\angle D=6x^{\circ }$

$\angle A+\angle B+\angle C+\angle D=360°$

(sum of angles of a quadrilateral)

$3x^{\circ }+4x^{\circ }+5x^{\circ }+6x^{\circ }={360}^{\circ }$​

$18x^{\circ }={360}^{\circ }$​​​​​​​​​​​​​​​​​​​​​

$x={20}^{\circ }$

$\Rightarrow \angle A={60}^{\circ }$

$\Rightarrow \angle B={80}^{\circ }$

$\Rightarrow \angle C={100}^{\circ }$

$\Rightarrow \angle D={120}^{\circ }$

$\angle B+\angle C={80}^{\circ }+{100}^{\circ }={180}^{\circ }$

Hence $DC\parallel AB$

ABCD is a trapezium