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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

given Angles of ABCD quadrilateral are in ratio 3:7:6:4 

Sum of angles in a quadrilateral is 360 

let angle A = 3x ,
     angle B = 7x 
     angle C = 6x 
    angle D = 4x
sum of angles = 360 
3x+7x+4x+6x =360
20x = 360 
x = 18 
A = 54  , B = 126 , C = 108 , D = 72 
it is not rhombus, parallelogram , kite as atleast one pair of angles to be equal for these quadrilateral.
therefore the quadrilateral can be a trapezium.
option c is correct

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