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 $∠ S$ = $110^{\circ}$ .

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Solution

The correct option is D
infinite

From the above diagram, it can be observed that we can draw side PQ = 4.5 cm and $∠ P$ = $70^{\circ}$ and $∠ Q$ = $100^{\circ}$ constructed. But it is not possible to fix points R and S since lengths of other sides aren't given. Hence, infinite quadrilaterals can be drawn just by satisfying $∠ R$ = $80^{\circ}$ and $∠ S$ = $110^{\circ}$ .

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

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 $∠ S$ = $110^{\circ}$ .