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Construct a Quadrilateral Abcd When Bc = 5.5 Cm, Cd = 4.1 Cm, ∠A = 70°, ∠B = 110° and ∠D = 85°. - Mathematics

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

Question

Construct a quadrilateral ABCD when BC = 5.5 cm, CD = 4.1 cm, ∠A = 70°, ∠B = 110° and ∠D = 85°.

Solution

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

\[i . e . , \angle A + \angle B + \angle C + \angle D = 360^\circ\]

\[ \Rightarrow \angle C = 95^\circ\]

Steps of construction: 

Step I: Draw BC = 5 . 5 cm . 

\[\text { Step II: Construct } \angle XBC = 110^\circ\text {  at A and }\angle BCY = 95^\circ . \]

Step III: With C as the centre and radius 4 . 1 cm, cut off CD = 4 . 1 cm . 

\[\text { Step IV: At D, draw } \angle CDZ = 85^\circ \text {P such that it meets BY at A } . \]

The quadrilateral so obtained is the required quadrilateral .

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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: 4 | Page no. 13
Solution Construct a Quadrilateral Abcd When Bc = 5.5 Cm, Cd = 4.1 Cm, ∠A = 70°, ∠B = 110° and ∠D = 85°. Concept: Constructing a Quadrilateral - When Two Adjacent Sides and Three Angles Are Known.
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