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  • If angles A, B, C and D of the 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

If angles A, B, C and D of the 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
 

Answers (1)

best_answer

Answer:   [C]

Solution. 
Given : 3 : 7 : 5 : 4 is the ratio of angles A, B, C, and D in a quadrilateral.
Let the angles be 3x, 7x, 6x and 4x.
As we know that the sum of angles is 360^{\circ}
3x+7x+6x+4x=360^{\circ}
20x=360^{\circ}
x=\frac{360^{\circ}}{20}=18^{\circ}
A=3x=3\times 18=54^{\circ}
B=7x=7\times 18=126^{\circ}
C=6x=6\times 18=108^{\circ}
D=4x=4\times 18=72^{\circ}
Now draw the quadrilateral with given angles.

Hence, BC\parallel AD and the sum of co-interior angles is 180^{\circ}
Hence ABCD is a trapezium

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