Question

The measurements of a quadrilateral are given as $AB=4cm,CD=5cm,\angle ABC={75}^{\circ },\angle BCD={45}^{\circ }$ and $\angle CDA={135}^{\circ }$.
Can you constant a unique quadrilateral ABCD?

• A. $\text{Yes}$
• B. $\text{No}$
• C. $\text{With the measure of}\angle DAB,\text{yes}$.
• D. $\text{With the measure of BC, yes}$.

Answer 1

The correct option is D $\text{With the measure of BC, yes}$.

The data gives us 3 angles and 2 sides, but the sides are not adjacent. Hence, the given quadrilateral is not unique.
On the other hand, we can construct a unique quadrilateral if we know the measure of BC, as we now have the measures of 2 adjacent sides and 3 angles.