Question

If the angles of a quadrilateral are in the ratio 3:4:6:7, then the quadrilateral is a___.

• A. Angles A & B
• B. Angles B & C
• C. Angles A & C
• D. Angles C & D

Answer 1

The correct option is D

Angles C & D

Let ABCD be the given quadrilateral let the angles of the quadrilateral be 3x,4x,6x and 7x.

$3x+4x+6x+7x={360}^{\circ }$ (sum of angles of a quadrilateral)

20x = 360

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

Therefore the angles are $3\left(18\right)=54,4\left(18\right)={72}^{\circ },6\left(18\right)={108}^{\circ }$ and $7\left(18\right)={126}^{\circ }$

Sum of adjancent angles ${72}^{\circ }+{108}^{\circ }={180}^{\circ }$

$\therefore AB||CD$ (Cointeriar angles are supplementary).

$\therefore ABCD$ is a trapezium. Hence (D)