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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