Question

The angles of a quadrilateral, in order, are in the ratio 4 : 4 :

5 : 5. This type of quadrilateral is a _____.

a) Parallelogram b) Rhombus

c) Rectangle d) Trapezium​

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.