NCERT Solutions for Class 8 Maths Chapter 3 Exercise 3.1

NCERT Solutions for Class 8 Maths Chapter 3 Exercise 3.1 – Understanding Quadrilaterals, has been designed by the NCERT to test the knowledge of the student on the following topics : 

  • Introduction
  • Polygons
    Classification of polygons
    Diagonals
    Convex and concave polygons
    Regular and irregular polygons
    Angle sum property

NCERT Solutions for Class 8 Maths Chapter 3 Exercise 3.1

NCERT Solutions for Class 8 Maths Chapter 3 Exercise 3.1 image 1




NCERT Solutions for Class 8 Maths Chapter 3 Exercise 3.1 image 2 NCERT Solutions for Class 8 Maths Chapter 3 Exercise 3.1 image 3




NCERT Solutions for Class 8 Maths Chapter 3 Exercise 3.1 image 4 NCERT Solutions for Class 8 Maths Chapter 3 Exercise 3.1 image 5




NCERT Solutions for Class 8 Maths Chapter 3 Exercise 3.1

1. Given here are some figures.

NCERT Solutions for Class 8 Maths Chapter 3 Exercise 3.1 Question 1

Classify each of them on the basis of the following

a) Simple curve
b) Simple closed curve
c) Polygon
d) Convex polygon
e) Concave polygon

Solution:

(a) Simple curves: 1, 2, 5, 6, 7
(b) Simple closed curves: 1, 2, 5, 6, 7
(c) Polygons: 1, 2
(d) Convex polygon: 2
(e) Concave polygon: 1

2. How many diagonals each of the following have?

(a) A convex quadrilateral
(b) A regular hexagon
(c) A triangle

Solution:

(a) A convex quadrilateral has 2 diagonals,
(b) A regular hexagon has 9 diagonals.
(c) A triangle has no diagonals.

3. What is the sum of the measures of angles of a convex quadrilateral? Will this property hold if the quadrilateral is not convex?

Solution:

A convex quadrilateral can be divided into two triangle by one of the diagonals
∴ Angle sum of convex quadrilateral
= Angle sum of two triangles
= 2 × 180°
= 360°
Similarly, a non-convex quadrilateral can also be divided into two triangles
Hence, the property holds true for non-convex quadrilaterals also.




4. Examine the table. (Each figure is divided into triangles and the sum of angles deduced from that.)

NCERT Solutions for Class 8 Maths Chapter 3 Exercise 3.1 Question 4

What can you say about the angle sum of a convex polygon with number of sides?

(a) 7
(b) 8
(c) 10
(d) n

Solution:

(a) Angle sum = (7 – 2) × 180° = 5 × 180° = 900°
(b) Angle sum = (8 – 2) × 180° = 6 × 180° = 1080°
(c) Angle sum = (10 – 2) × 180° = 8 × 180° = 1440°
(d) Angle sum = (n – 2) × 180°

5. What is a regular polygon?
State the name of a regular polygon of

(i) 3 sides
(ii) 4 sides
(iii) 6 sides

Solution:

A polygon with equal sides and equal angles is called a regular polygon.

(i) A regular polygon of 3 sides is called an equilateral triangle.
(ii) A regular polygon of 4 sides is called a square.
(iii) A regular polygon of 6 sides is called a regular hexagon.

6. Find the angle measure x in the following figures

a)

NCERT Solutions for Class 8 Maths Chapter 3 Exercise 3.1 Question 6a 

Solution:

Using angle sum property of quadrilateral
50° + 130° + 120° + x = 360°
300° + x = 360°
x = 60°

b) 

NCERT Solutions for Class 8 Maths Chapter 3 Exercise 3.1 Question 6b

Solution:

Using angle sum property of quadrilateral
70° + 60° + 90° + x = 360°
220° + x = 360°
x = 360° – 220°
x = 140°

c)

NCERT Solutions for Class 8 Maths Chapter 3 Exercise 3.1 Question 6c 

Solution:

The interior angles of the base of the pentagon will be 110°(= 180° – 70°) and 120°(= 180° – 60°)

Angle sum of pentagon = (5 – 2) × 180° = 3 × 180° = 540°
30° + x + 110° + 120° + x = 540°
260° + 2x = 540°
2x = 540° – 260°
2x = 280°
x = 140°




d) 

NCERT Solutions for Class 8 Maths Chapter 3 Exercise 3.1 Question 6d

Solution:

Angle sum of pentagon = (5 – 2) × 180° = 3 × 180° = 540°

x + x + x + x + x = 540°
5x = 540°
x = 108°

7. (a) Find x + y + z

NCERT Solutions for Class 8 Maths Chapter 3 Exercise 3.1 Question 7a

Solution:

Exterior angle = 180° – Interior angle
∴ z = 180° – 30° = 150°
x = 180° – 90° = 90°

Interior angle = 180° – Exterior angle
∴ Unknown interior angle of triangle = 180° – y

Using angle sum property of triangle
90° + 30° + (180° – y) = 180°
y = 90° + 30° + 180° – 180°
y = 90° + 30°
y = 120°
Therefore, x + y + z = 90° + 120° + 150° = 360°

(b) Find x + y + z + w

NCERT Solutions for Class 8 Maths Chapter 3 Exercise 3.1 Question 7b

Solution:

Exterior angle = 180° – Interior angle
∴ x = 180° – 120° = 60°
y = 180° – 80° = 100°
z = 180° – 60° = 120°

Interior angle = 180° – Exterior angle
∴ Unknown interior angle of quadrilateral = 180° – w

Angle sum of quadrilateral = (4 – 2) × 180° = 2 × 180° = 360°
60° + 80° + 120° + (180° – w) = 360°
w = 60° + 80° + 120° + 180° – 360°
w = 440° – 360°
w = 80°

Therefore, x + y + z + w = 60° + 100° + 120° + 80° = 360°

The next Exercise for NCERT Solutions for Class 8 Maths Chapter 3 Exercise 3.2 – Understanding Quadrilaterals can be accessed by clicking here

Download NCERT Solutions for Class 8 Maths Chapter 3 Exercise 3.1 – Understanding Quadrilaterals

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