Question

If $\angle A,\angle B,\angle Cand\angle D$ 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

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 = ${18}^{\circ }$
A = ${54}^{\circ }$ , B = ${126}^{\circ }$ , C = ${108}^{\circ }$ , D = ${72}^{\circ }$
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