The measurements of a quadrilateral are given as AB -4 cm - CD -5 cm - - ABC -75- - BCD -45- and - CDA -135- - Can you construct aunique quadrilateral ABCD-A- YesB- NoC- With the measure of - DAB- yes-D- With the measure of BC- yes-

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Construction of Quadrilateral 2 Adjacent Sides and 3 Angles Are Given

The measureme...

Question

The measurements of a quadrilateral are given as AB $= 4 c m$ , CD $= 5 c m$ , $∠$ ABC $= 75^{\circ}$ , $∠$ BCD $= 45^{\circ}$ and $∠$ CDA $= 135^{\circ}$ . Can you construct a unique quadrilateral ABCD?

Yes

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With the measure of

∠ D A B

, yes.

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With the measure of BC, yes.

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Solution

The correct option is D With the measure of BC, yes.
The data gives us 3 angles and 2 sides, but the sides are not adjacent. Hence, the given quadrilateral is not unique.
On the other hand, we can construct a unique quadrilateral if we know the measure of BC, as we now have the measures of 2 adjacent sides and 3 angles.

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The measurements of a quadrilateral are given as AB =4 cm, CD =5 cm, ∠ABC =75∘, ∠BCD =45∘ and ∠CDA =135∘. Can you construct a unique quadrilateral ABCD?

The measurements of a quadrilateral are given as AB $= 4 c m$ , CD $= 5 c m$ , $∠$ ABC $= 75^{\circ}$ , $∠$ BCD $= 45^{\circ}$ and $∠$ CDA $= 135^{\circ}$ . Can you construct a unique quadrilateral ABCD?