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Construct a Quadrilateral Pqrs, Where Pq = 3.5 Cm, Qr = 6.5 Cm, ∠P = ∠R = 105° and ∠S = 75°. - Mathematics

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ConceptConstructing a Quadrilateral When Two Adjacent Sides and Three Angles Are Known

Question

Construct a quadrilateral PQRS, where PQ = 3.5 cm, QR = 6.5 cm, ∠P = ∠R = 105° and ∠S = 75°.

Solution

We know that the sum of all the angles in a quadrilateral is 360 . 

i . e . , ∠P + ∠Q + ∠R + ∠S = 360°

⇒ ∠Q = 75°

Steps of construction: 

Step I: Draw PQ = 3 . 5 cm . 

Step II: Construct ∠XPQ = 105° at P and ∠PQY = 75° at Q . 

Step III: With Q as the centre and radius 6 . 5 cm, cut off QR = 6 . 5

Step IV: At R, draw ∠QRZ = 105° such that it meets PX at S . 

The quadrilateral so obtained is the required quadrilateral .

  Is there an error in this question or solution?

APPEARS IN

 RD Sharma Solution for Mathematics for Class 8 by R D Sharma (2019-2020 Session) (2017 to Current)
Chapter 18: Practical Geometry (Constructions)
Ex. 18.5 | Q: 3 | Page no. 13
Solution Construct a Quadrilateral Pqrs, Where Pq = 3.5 Cm, Qr = 6.5 Cm, ∠P = ∠R = 105° and ∠S = 75°. Concept: Constructing a Quadrilateral - When Two Adjacent Sides and Three Angles Are Known.
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