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
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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
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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.