Question

The angles of a quadrilateral are in the ratio 2 : 3 : 2 : 3 taken in order. The quadrilateral is always a

• A. Rhombus
• B. Kite
• C. Parallelogram
• D. Rectangle

Answer 1

The correct option is C Parallelogram

Given that the angles of a quadrilateral are in the ratio 2 : 3 : 2 : 3 taken in order.
Let the angles of the quadrilateral ABCD be $\angle A=2K,\angle B=3K,\angle C=2K$ and $\angle D=3K$, where K is any natural number.
$\Rightarrow \angle A=\angle C$ and $\angle B=\angle D$
Since in a parallelogram, the opposite angles are equal.
Therefore, the quadrilateral ABCD is a parallelogram.
The angles of the quadrilateral do not imply anything about the measure of the sides of the quadrilateral.
Thus, it cannot be concluded that it is a rhombus or a rectangle.
Hence, the correct answer is option (c).