Given, ratio of angles of quadrilateral ABCD is 3: 7: 6: 4
Let angles of quadrilateral ABCD be 3x, 7x, 6x and 4x, respectively.
We know that, sum of all angles of a quadrilateral is 360∘.
∴3x+7x+6x+4x=360∘⇒20x=360∘⇒x=360∘20∘=18∘
∴ Angles of the quadrilateral are
∠A=3×18=54∘∠B=7×18=126∘∠C=6×18=108∘
And ∠D=4×18=72∘
From figure, ∠BCE=180∘−∠BCD [linear pair axiom]
⇒∠BCE=180∘−108∘=72∘
Since, the corresponding angles are equal .
∴BC||AD
Now, sum of cointerior angles,
∠A+∠B=126∘+54∘=180∘
and ∠C+∠D=108∘+72∘=180∘
Hence, ABCD is a trapezium.