We cannot construct a quadrilateral PQRS with PQ -6 cm - QR -5 cm - - P -70- - Q -150- and the measurement of - R asA- 70-B- 100-C- 80-D- 140-

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Construction of Quadrilateral Given 3 Sides and 2 Included Angles

We cannot con...

Question

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

70^o

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100^o

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80^o

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140^o

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Solution

The correct option is D
140^o

We know: Sum of all the angles in a quadrilateral is 360^o.
If ∠R = 140°, then

∠P + ∠Q + ∠R + ∠S = 360^o

70^o + 150^o + 140° + ∠S = 360^o

360^o + ∠S = 360^o

∠S = 0^o

Hence, a quadrilateral cannot be constructed with the given measurements and measure of ∠R as 140^o.

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

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