How many quadrilaterals can I construct with the following data: Quadrilateral PQRS with PQ = 4.5 cm, Angle P = $70^{\circ}$ , Angle Q = $100^{\circ}$ , Angle R = $80^{\circ}$ and Angle S = $80^{\circ}$ .

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Solution

The correct option is D
infinite

From above diagram, it can be observed that side PQ can be constructed and angles P and Q can be drawn. But it is not possible to fix points R and S. Hence, infinite quadrilaterals can be drawn fixing points P and Q wherever required according to angles R and S.

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How many quadrilaterals can we construct with the following data: quadrilateral PQRS with PQ = 4.5 cm, $∠ P$ = $70^{\circ}$ , $∠ Q$ = $100^{\circ}$ , $∠ R$ = $80^{\circ}$ and $∠ S$ = $110^{\circ}$ .

Q. Can we draw a quadrilateral uniquely with the following data? Suppose that, PQRS is the quadrilateral with PQ = 4 cm,

∠ P

80^{\circ}

∠ Q

105^{\circ}

∠ R

80^{\circ}

We cannot construct a quadrilateral PQRS with PQ =6cm, QR = 5 cm, ∠P = 70^o, ∠Q = 150^o and the measurement of ∠R as

Q. Construct a cyclic quadrilateral PQRS with PQ

= 4

cm,

∠

= 100^{o}

∠

PQS

= 40^{o}

and

∠

SQR

= 70^{o}

Q. Construct a quadrilateral

P Q R S

such that

P Q = 3.5 c m, Q R = 4.5 c m, R S = 4 c m, ∠ Q = 110^{o}

and

∠ R = 80^{o}

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How many quadrilaterals can I construct with the following data: Quadrilateral PQRS with PQ = 4.5 cm, Angle P = 70∘, Angle Q = 100∘, Angle R = 80∘ and Angle S =80∘.

The correct option is D infinite From above diagram, it can be observed that side PQ can be constructed and angles P and Q can be drawn. But it is not possible to fix points R and S. Hence, infinite quadrilaterals can be drawn fixing points P and Q wherever required according to angles R and S.

How many quadrilaterals can I construct with the following data: Quadrilateral PQRS with PQ = 4.5 cm, Angle P = $70^{\circ}$ , Angle Q = $100^{\circ}$ , Angle R = $80^{\circ}$ and Angle S = $80^{\circ}$ .

The correct option is D
infinite

From above diagram, it can be observed that side PQ can be constructed and angles P and Q can be drawn. But it is not possible to fix points R and S. Hence, infinite quadrilaterals can be drawn fixing points P and Q wherever required according to angles R and S.