Question

If measure of sides of a quadrilateral are given as AB = 4cm, CD = 5cm, and angles are given as $\angle ABC={75}^{\circ },\angle BCD={45}^{\circ }and\angle CDA={135}^{\circ }$, then what additional information is required to 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 C

With the measure of ∠DAB, 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.