Question

If measure of sides of a quadrilateral are given as AB = 4 cm, CD = 5 cm, and angles are given as ∠ ABC = ${75}^{\circ }$, ∠ BCD = ${35}^{\circ }$ and ∠ CDA = ${135}^{\circ }$, can you construct a quadrilateral ABCD?

• A. Yes
• B. No
• C. With the measure of ∠DAB, Yes
• D. With the measure of BC, Yes

Answer 1

The correct option is D

With the 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 to construct the quadrilateral ABCD. But with BC, we will have 6 sets of measurements and two known adjacent sides. Hence, we will be able to construct the quadrilateral ABCD.