Question

if angles A,B,C,D of the quadrilateral ABCD, taken in order, are in the ratio 1 ratio 1 ratio 1 ratio 1 then ABCD is a...... options a) square b)Rhombus c) rectangle d) 1 and 3​

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 Rhombus