RD Sharma Solutions for Class 8 Maths Chapter 18 Practical Geometry (Constructions) Exercise 18.5

Exercise 18.5 Chapter 18 of RD Sharma details the concept of construction of a quadrilateral when its three angles and their two included sides are given. The procedures to construct a quadrilateral are provided here with steps to help students prepare well for the final exam. For further assistance, students can refer to RD Sharma Class 8 Solutions formulated by the subject experts at BYJU’S with all the shortcut methods to solve any question. For better understanding, students can download the PDF from the links provided below.

RD Sharma Solutions for Class 8 Maths Exercise 18.5 Chapter 18 Practical Geometry (Constructions)

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Access answers to RD Sharma Maths Solutions for Class 8 Exercise 18.5 Chapter 18 Practical Geometry (Constructions)

1. Construct a quadrilateral ABCD given that AB = 4 cm, BC = 3 cm, ∠A = 75°, ∠B = 80° and ∠C = 120°.

Solution:

The given details are AB = 4 cm, BC = 3 cm, ∠A = 75°, ∠B = 80° and ∠C = 120°.

Steps to construct a quadrilateral:

Step 1- Draw a line AB = 4cm

Step 2- Construct an angle of 75^o at A.

Step 3- Construct an angle of 80^o at B.

Step 4- Cut an arc of radius 3cm with B as the centre to mark that point as C.

Step 5- Construct an angle of 120^o at C such that it meets the line segment AX, mark that point as D.

Step 6- Now join BC, CD and DA.

2. Construct a quadrilateral ABCD where AB = 5.5 cm, BC = 3.7 cm, ∠A = 60°, ∠B = 105° and ∠D = 90°.

Solution:

The given details are AB = 5.5 cm, BC = 3.7 cm, ∠A = 60°, ∠B = 105° and ∠D = 90°.

We know that ∠A + ∠B + ∠C + ∠D = 360^o

∴ ∠C = 105^o

Steps to construct a quadrilateral:

Step 1- Draw a line AB = 5.5cm

Step 2- Construct an angle of 60^o at A.

Step 3- Construct an angle of 105^o at B.

Step 4- Cut an arc of radius 3.7cm with B as the centre to mark that point as C.

Step 5- Construct an angle of 105^o at C such that it meets the line segment AX, mark that point as D.

Step 6- Now join BC, CD and DA.

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

Solution:

The given details are PQ = 3.5 cm, QR = 6.5 cm, ∠P = ∠R = 105° and ∠S = 75°.

We know that ∠P + ∠Q + ∠R + ∠S = 360^o

∴ ∠Q = 75^o

Steps to construct a quadrilateral:

Step 1- Draw a line PQ = 3.5cm

Step 2- Construct an angle of 105^o at P.

Step 3- Construct an angle of 75^o at Q.

Step 4- Cut an arc of radius 6.5cm with Q as the centre to mark that point as R.

Step 5- Construct an angle of 105^o at R such that it meets the line segment PX, mark that point as S.

Step 6- Now join QR, RS and PS.

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

Solution:

The given details are BC = 5.5 cm, CD = 4.1 cm, ∠A = 70°, ∠B = 110° and ∠D = 85°.

We know that ∠A + ∠B + ∠C + ∠D = 360^o

∴ ∠C = 95^o

Steps to construct a quadrilateral:

Step 1- Draw a line BC = 5.5cm

Step 2- Construct an angle of 110^o at B.

Step 3- Construct an angle of 95^o at C.

Step 4- Cut an arc of radius 4.1cm with C as the centre to mark that point as D.

Step 5- Construct an angle of 85^o at D such that it meets the line segment BX, mark that point as A.

Step 6- Now join CD, DA and BA.

5. Construct a quadrilateral ABCD ∠A = 65°, ∠B = 105°, ∠C = 75°, BC = 5.7 cm and CD = 6.8 cm.

Solution:

The given details are ∠A = 65°, ∠B = 105°, ∠C = 75°, BC = 5.7 cm and CD = 6.8 cm.

We know that ∠A + ∠B + ∠C + ∠D = 360^o

∴ ∠D = 115^o

Steps to construct a quadrilateral:

Step 1- Draw a line BC = 5.7cm

Step 2- Construct an angle of 105^o at B.

Step 3- Construct an angle of 75^o at C.

Step 4- Cut an arc of radius 6.8cm with C as the centre to mark that point as D.

Step 5- Construct an angle of 115^o at D such that it meets the line segment BX, mark that point as A.

Step 6- Now join CD, DA and BA

6. Construct a quadrilateral PQRS in which PQ = 4 cm, QR = 5 cm ∠P = 50°, ∠Q = 110° and ∠R = 70°.

Solution:

The given details are PQ = 4 cm, QR = 5 cm ∠P = 50°, ∠Q = 110° and ∠R = 70°.

Steps to construct a quadrilateral:

Step 1- Draw a line PQ = 4cm

Step 2- Construct an angle of 50^o at P.

Step 3- Construct an angle of 110^o at Q.

Step 4- Cut an arc of radius 5cm with Q as the centre to mark that point as R.

Step 5- Construct an angle of 70^o at R, such that it meets the line segment PX, mark that point as S.

Step 6- Now join QR, RS and PS.