Question

The angles of a quadrilateral are in the ratio $3:4:5:6$. The quadrilateral is a _____

• A. Parallelogram
• B. Rectangle
• C. Square
• D. Trapezium

Answer 1

Answer: (D)

Trapezium

Given that angles of a quadrilateral are in the ration $3:4:5:6$.

We know that sum of all angles of a quadrilateral $={360}^0$.

So, angles of quadrilateral are:

$\angle A=\frac{3}{18}\times 360=60,\angle B=\frac{4}{18}\times 360=80,\angle C=\frac{5}{18}\times 360=100,\angle D=\frac{6}{18}\times 360=120$

Now from figure, we have

$\angle A+\angle D=60+120=180$

i.e. sum of interior angles on the same side of the transversal $AD={180}^0$.

Therefore, $AB\parallel DC$

Hence, the given quadrilateral is a trapezium.