If measure of sides of a quadrilateral are given as AB = 4cm, CD = 5

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

Options:

A . Yes

B . No

C . With the measure of

∠

DAB, Yes

D . With the measure of BC, Yes

Answer: Option D
:
D

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.

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