If the measurement of sides of a quadrilateral are given as AB = 4cm, CD = 5 cm, and angles are given as ∠ABC= 75∘, ∠BCD= 45∘ and ∠CDA= 135∘, can you construct a unique quadrilateral ABCD?
With measure of BC, Yes
We can't draw a unique quadrilateral with all the measurements, which are given. This is because we need the measurement of two adjacent sides and 3 angles for the construction of a unique quadrilateral. But with BC, we will have 6 sets of measurements and two known adjacent sides. Hence, we will be able to construct a unique quadrilateral in this case.