Question

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

(a) rhombus 

(b) parallelogram 

(c) trapezium 

(d) kite

Answer 1

(c) trapezium

Let the angles of the quadrilateral be 3\(x\), 7\(x\), 6\(x\) and 4\(x\). 

Then, 3\(x\) + 7\(x\) + 6\(x\) + 4\(x\) = 360° 

⇒ 20\(x\) = 360° ⇒ \(x\) = 18° 

∴ The angles A, B, C and D are respectively 3 x 18°, 7 x 18°, 6 x 18° and 4 x 18°, i.e.,54°, 126°, 108° and 72°.

which shows that ∠A + ∠B = 180° and ∠C + ∠D = 180° ⇒ AD||BC. 

Hence ABCD is a trapezium.