Question

How many quadrilaterals can I construct with the following data: Quadrilateral PQRS with PQ = 4.5 cm, Angle P = ${70}^{\circ }$, Angle Q = ${100}^{\circ }$, Angle R = ${80}^{\circ }$ and Angle S =${110}^{\circ }$.

• A. 0
• B. 1
• C. 2
• D. Infinite

Answer 1

The correct option is D

Infinite

From above diagram, it can be observed that side PQ can be constructed and angles P and Q can be drawn. But it is not possible to locate points R and S as their lengths are not known. Hence, infinite quadrilaterals can be drawn.

And we know that to construct an unique quardilateral, we need the measures of either of the options stated below:

• 4 sides and 1 diagonal​
• 3 sides and 2 included angles
• 3 sides and 2 diagonal
• 2 adjacent sides and 3 angles​
• 4 sides and 1 angle​

But here we are given 1 side and 4 angles which is not in the above options. Hence, there can be infinite number of ways to construct this quadrilateral.