Question

Let us say you are required to construct a quadrilateral $ABCD$ where the measurements are $AB=5\text{cm},BC=3\text{cm},\angle A=120°,\angle B=110°,$ and $\angle C=130°$.
A quadrilateral with the above specifications will be in the shape of:

• A. Cannot construct a quadrilateral with the given specifications
• B. Parallelogram
• C. Square
• D. Trapezium

Answer 1

The correct option is A Cannot construct a quadrilateral with the given specifications

According to the angle sum property of quadrilaterals, the sum of all $4$ angles should be equal to ${360}^{\circ }$.
Here, the sum of $3$ given angles is ${360}^{\circ }$ only and the fourth angle cannot be $0^{\circ }$.
So, the construction of quadrilaterals with the above specifications is not possible.