Question

If the measurement of sides of a quadrilateral are given as AB = 4cm, CD = 5 cm, and angles are given as $\angle ABC=$ ${75}^{\circ }$, $\angle BCD=$ ${45}^{\circ }$ and $\angle CDA=$ ${135}^{\circ }$, can you construct a unique quadrilateral ABCD?

• A. Yes
• B. No
• C. With measure of $\angle DAB$, Yes
• D. With measurement of BC, Yes

Answer 1

The correct option is D

With measurement 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.