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