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RD Sharma Solutions for Class 8 Maths Chapter 18 
– Practical Geometry (Constructions) 
 
EXERCISE 18.5                                                 PAGE NO: 18.13 
 
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 and angle of 75
o
 at A. 
Step 3- Construct and angle of 80
o
 at B. 
Step 4- Cut an arc of radius 3cm with B as the center to mark that point as C. 
Step 5- Construct and 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 and angle of 60
o
 at A. 
Step 3- Construct and angle of 105
o
 at B. 
Page 2


 
 
 
 
RD Sharma Solutions for Class 8 Maths Chapter 18 
– Practical Geometry (Constructions) 
 
EXERCISE 18.5                                                 PAGE NO: 18.13 
 
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 and angle of 75
o
 at A. 
Step 3- Construct and angle of 80
o
 at B. 
Step 4- Cut an arc of radius 3cm with B as the center to mark that point as C. 
Step 5- Construct and 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 and angle of 60
o
 at A. 
Step 3- Construct and angle of 105
o
 at B. 
 
 
 
 
RD Sharma Solutions for Class 8 Maths Chapter 18 
– Practical Geometry (Constructions) 
 
Step 4- Cut an arc of radius 3.7cm with B as the center to mark that point as C. 
Step 5- Construct and 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 and angle of 105
o
 at P. 
Step 3- Construct and angle of 75
o
 at Q. 
Step 4- Cut an arc of radius 6.5cm with Q as the center to mark that point as R. 
Step 5- Construct and 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 
Page 3


 
 
 
 
RD Sharma Solutions for Class 8 Maths Chapter 18 
– Practical Geometry (Constructions) 
 
EXERCISE 18.5                                                 PAGE NO: 18.13 
 
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 and angle of 75
o
 at A. 
Step 3- Construct and angle of 80
o
 at B. 
Step 4- Cut an arc of radius 3cm with B as the center to mark that point as C. 
Step 5- Construct and 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 and angle of 60
o
 at A. 
Step 3- Construct and angle of 105
o
 at B. 
 
 
 
 
RD Sharma Solutions for Class 8 Maths Chapter 18 
– Practical Geometry (Constructions) 
 
Step 4- Cut an arc of radius 3.7cm with B as the center to mark that point as C. 
Step 5- Construct and 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 and angle of 105
o
 at P. 
Step 3- Construct and angle of 75
o
 at Q. 
Step 4- Cut an arc of radius 6.5cm with Q as the center to mark that point as R. 
Step 5- Construct and 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 
 
 
 
 
RD Sharma Solutions for Class 8 Maths Chapter 18 
– Practical Geometry (Constructions) 
 
 
 
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 and angle of 110
o
 at B. 
Step 3- Construct and angle of 95
o
 at C. 
Step 4- Cut an arc of radius 4.1cm with C as the center to mark that point as D. 
Step 5- Construct and 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 
Page 4


 
 
 
 
RD Sharma Solutions for Class 8 Maths Chapter 18 
– Practical Geometry (Constructions) 
 
EXERCISE 18.5                                                 PAGE NO: 18.13 
 
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 and angle of 75
o
 at A. 
Step 3- Construct and angle of 80
o
 at B. 
Step 4- Cut an arc of radius 3cm with B as the center to mark that point as C. 
Step 5- Construct and 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 and angle of 60
o
 at A. 
Step 3- Construct and angle of 105
o
 at B. 
 
 
 
 
RD Sharma Solutions for Class 8 Maths Chapter 18 
– Practical Geometry (Constructions) 
 
Step 4- Cut an arc of radius 3.7cm with B as the center to mark that point as C. 
Step 5- Construct and 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 and angle of 105
o
 at P. 
Step 3- Construct and angle of 75
o
 at Q. 
Step 4- Cut an arc of radius 6.5cm with Q as the center to mark that point as R. 
Step 5- Construct and 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 
 
 
 
 
RD Sharma Solutions for Class 8 Maths Chapter 18 
– Practical Geometry (Constructions) 
 
 
 
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 and angle of 110
o
 at B. 
Step 3- Construct and angle of 95
o
 at C. 
Step 4- Cut an arc of radius 4.1cm with C as the center to mark that point as D. 
Step 5- Construct and 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 
RD Sharma Solutions for Class 8 Maths Chapter 18 
– Practical Geometry (Constructions)
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 and angle of 105
o
 at B.
Step 3- Construct and angle of 75
o
 at C.
Step 4- Cut an arc of radius 6.8cm with C as the center to mark that point as D.
Step 5- Construct and 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
Page 5


 
 
 
 
RD Sharma Solutions for Class 8 Maths Chapter 18 
– Practical Geometry (Constructions) 
 
EXERCISE 18.5                                                 PAGE NO: 18.13 
 
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 and angle of 75
o
 at A. 
Step 3- Construct and angle of 80
o
 at B. 
Step 4- Cut an arc of radius 3cm with B as the center to mark that point as C. 
Step 5- Construct and 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 and angle of 60
o
 at A. 
Step 3- Construct and angle of 105
o
 at B. 
 
 
 
 
RD Sharma Solutions for Class 8 Maths Chapter 18 
– Practical Geometry (Constructions) 
 
Step 4- Cut an arc of radius 3.7cm with B as the center to mark that point as C. 
Step 5- Construct and 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 and angle of 105
o
 at P. 
Step 3- Construct and angle of 75
o
 at Q. 
Step 4- Cut an arc of radius 6.5cm with Q as the center to mark that point as R. 
Step 5- Construct and 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 
 
 
 
 
RD Sharma Solutions for Class 8 Maths Chapter 18 
– Practical Geometry (Constructions) 
 
 
 
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 and angle of 110
o
 at B. 
Step 3- Construct and angle of 95
o
 at C. 
Step 4- Cut an arc of radius 4.1cm with C as the center to mark that point as D. 
Step 5- Construct and 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 
RD Sharma Solutions for Class 8 Maths Chapter 18 
– Practical Geometry (Constructions)
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 and angle of 105
o
 at B.
Step 3- Construct and angle of 75
o
 at C.
Step 4- Cut an arc of radius 6.8cm with C as the center to mark that point as D.
Step 5- Construct and 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
 
 
 
 
RD Sharma Solutions for Class 8 Maths Chapter 18 
– Practical Geometry (Constructions) 
 
 
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 and angle of 50
o
 at P. 
Step 3- Construct and angle of 110
o
 at Q. 
Step 4- Cut an arc of radius 5cm with Q as the center to mark that point as R. 
Step 5- Construct and 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

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