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

The NCERT Solutions for Class 8 Maths Chapter 3 – Understanding Quadrilaterals contains solutions for all exercise questions. The subject experts at BYJU’S have solved each question of NCERT exercises meticulously to help the students in solving the questions from the NCERT textbook. NCERT Class 8 Exercise 3.1 is based on polygons and the classification of polygons. Students can download the NCERT Solutions of Class 8 Mathematics to sharpen their skills.

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

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Access Other Exercise Solutions of Class 8 Maths Chapter 3 – Understanding Quadrilaterals

Exercise 3.2 Solutions 6 Questions (6 Short Answer Questions)

Exercise 3.3 Solutions 12 Questions (6 Long Answer Questions, 6 Short Answer Questions)

Exercise 3.4 Solutions 6 Questions (1 Long Answer Question, 5 Short Answer Questions)

Access Answers to NCERT Class 8 Maths Chapter 3 – Understanding Quadrilaterals Exercise 3.1 Page Number 41

1. Given here are some figures.

Classify each of them on the basis of the following.

Simple curve (b) Simple closed curve (c) Polygon

(d) Convex polygon (e) Concave polygon

Solution:

a) Simple curve: 1, 2, 5, 6 and 7

b) Simple closed curve: 1, 2, 5, 6 and 7

c) Polygon: 1 and 2

d) Convex polygon: 2

e) Concave polygon: 1

2. How many diagonals does each of the following have?

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

Solution:

a) A convex quadrilateral: 2.

b) A regular hexagon: 9.

c) A triangle: 0

3. What is the sum of the measures of the angles of a convex quadrilateral? Will this property hold if the quadrilateral is not convex? (Make a non-convex quadrilateral and try)

Solution:

Let ABCD be a convex quadrilateral.

From the figure, we infer that the quadrilateral ABCD is formed by two triangles,

i.e. ΔADC and ΔABC.

Since we know that sum of the interior angles of a triangle is 180°,

the sum of the measures of the angles is 180° + 180° = 360°

Let us take another quadrilateral ABCD which is not convex.

Join BC, such that it divides ABCD into two triangles, ΔABC and ΔBCD. In ΔABC,

∠1 + ∠2 + ∠3 = 180° (angle sum property of triangle)

In ΔBCD,

∠4 + ∠5 + ∠6 = 180° (angle sum property of triangle)

∴, ∠1 + ∠2 + ∠3 + ∠4 + ∠5 + ∠6 = 180° + 180°

⇒ ∠1 + ∠2 + ∠3 + ∠4 + ∠5 + ∠6 = 360°

⇒ ∠A + ∠B + ∠C + ∠D = 360°

Thus, this property holds if the quadrilateral is not convex.

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

What can you say about the angle sum of a convex polygon with the number of sides? (a) 7 (b) 8 (c) 10 (d) n

Solution:

The angle sum of a polygon having side n = (n-2)×180°

a) 7

Here, n = 7

Thus, angle sum = (7-2)×180° = 5×180° = 900°

b) 8

Here, n = 8

Thus, angle sum = (8-2)×180° = 6×180° = 1080°

c) 10

Here, n = 10

Thus, angle sum = (10-2)×180° = 8×180° = 1440°

d) n

Here, n = n

Thus, 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:

Regular polygon: A polygon having sides of equal length and angles of equal measure is called a regular polygon, i.e. a regular polygon is both equilateral and equiangular.

(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.

Solution:

a) The figure has 4 sides. Hence, it is a quadrilateral. Sum of angles of the quadrilateral = 360°

⇒ 50° + 130° + 120° + x = 360°

⇒ 300° + x = 360°

⇒ x = 360° – 300° = 60°

b) The figure has 4 sides. Hence, it is a quadrilateral. Also, one side is perpendicular, forming a right angle.

Sum of angles of the quadrilateral = 360°

⇒ 90° + 70° + 60° + x = 360°

⇒ 220° + x = 360°

⇒ x = 360° – 220° = 140°

c) The figure has 5 sides. Hence, it is a pentagon.

Sum of angles of the pentagon = 540°

Two angles at the bottom are linear pairs.

∴, 180° – 70° = 110°

180° – 60° = 120°

⇒ 30° + 110° + 120° + x + x = 540°

⇒ 260° + 2x = 540°

⇒ 2x = 540° – 260° = 280°

⇒ 2x = 280°

= 140°

d) The figure has 5 equal sides. Hence, it is a regular pentagon.

Thus, its all angles are equal.

5x = 540°

⇒ x = 540°/5

⇒ x = 108°

7.

Solution:

a) Sum of all angles of the triangle = 180°

One side of triangle = 180°- (90° + 30°) = 60°

x + 90° = 180° ⇒ x = 180° – 90° = 90°

y + 60° = 180° ⇒ y = 180° – 60° = 120°

z + 30° = 180° ⇒ z = 180° – 30° = 150°

x + y + z = 90° + 120° + 150° = 360°

b) Sum of all angles of quadrilateral = 360°

One side of quadrilateral = 360°- (60° + 80° + 120°) = 360° – 260° = 100°

x + 120° = 180° ⇒ x = 180° – 120° = 60°

y + 80° = 180° ⇒ y = 180° – 80° = 100°

z + 60° = 180° ⇒ z = 180° – 60° = 120°

w + 100° = 180° ⇒ w = 180° – 100° = 80°

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

Exercise 3.1 of NCERT Solutions for Class 8 Maths Chapter 3 – Understanding Quadrilaterals is based on the following topics:

1. Introduction
2. Polygons
   1. Classification of Polygons
   2. Diagonals
   3. Convex and Concave Polygons
   4. Regular and Irregular Polygons
   5. Angle Sum Property

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NCERT Solutions for Class 8 Maths

NCERT Solutions for Class 8