Question

If ∠A, ∠B, ∠C and ∠D of a quadrilateral ABCD taken in order, are in the ratio 3 : 7 : 6 : 4, then ABCD is a
(a) rhombus
(b) kite
(c) trapezium
(d) parallelogram

Answer 1

(c) Trapezium

Explanation:

Let the angles be (3x), (7x), (6x) and (4x)​.
Then 3x + 7x + 6x + 4x = 360^o
∴ x = 18^o
​Thus, the angles are 3 ⨯18^o = 54^o, ​7 ⨯ 18^o = 126^o, ​6 ⨯ 18^o = 108^o and ​4 ⨯18^o = 72^o.
But 54^o + 126^o = 180^o and 72^o + 108^o = 180^o
∴ ABCD is a trapezium.