Question

If angles A, B C, D of quadrilateral ABCB , taken in order, are in the ratio 3:7:6:4 , then ABCD is

1.rhombus
2.Parallelogram
3.Trapezium
4.Kite

Answer 1

Answer:

Let the angles of the quadrilateral be 3x,7x,6x and 4x.

Then, 3x+7x+6x+4x=360∘

⇒20x=360∘

⇒x=18∘

Therefore, the angles A,B,C and D are respectively

∠A=3×18=54,∠B=7×18=126,∠C=6×18=108,∠D=4×18=72.

which shows that ∠A+∠B=180∘ and ∠C+∠D=180∘ →AD∣∣BC.

Hence ABCD is a trapezium.

Hope this is helpful for you.