NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Ex 3.1

NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Ex 3.1 are part of NCERT Solutions for Class 8 Maths. Here we have given NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Ex 3.1.

• Understanding Quadrilaterals Class 8 Ex 3.2
• Understanding Quadrilaterals Class 8 Ex 3.3
• Understanding Quadrilaterals Class 8 Ex 3.4

Board	CBSE
Textbook	NCERT
Class	Class 8
Subject	Maths
Chapter	Chapter 3
Chapter Name	Understanding Quadrilaterals
Exercise	Ex 3.1
Number of Questions Solved	7
Category	NCERT Solutions

NCERT Solutions for Class 8 Maths Chapter 3 Understanding Quadrilaterals Ex 3.1

Ex 3.1 Class 8 Maths Question 1.
Given here are some figures :

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.
The classification of the given figures is as under :
(a) Simple curve : (1), (2), (5), (6), (7) and (8)
(b) Simple closed curve : (1), (2), (5), (6) and (7)
(c) Polygon: (1) and (2)
(d) Convex polygon : (2)
(e) Concave polygon : (1) and (4)

Ex 3.1 Class 8 Maths Question 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 has two diagonals.
(b) A regular hexagon has nine diagonals.
(c) A triangle has no diagonal.

Ex 3.1 Class 8 Maths Question 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 j try!)
Solution.
The sum of measures of the angles of a convex quadrilateral is 360°. Yes, this property holds in case of the quadrilateral is not convex.

Ex 3.1 Class 8 Maths Question 4.
Examine the table. (Each figure is divided into triangles and the sum of the angles deduced from that.)

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.
From the given table, dearly we observe that the sum of angles (interior angles) of a polygon with n sides = (n – 2) x 180°.
(a) n = 7
∴ The sum of the angles of a polygon of 7 sides
Angle sum =
=

(b) n = 8
∴ The sum of the angles of a polygon of 8 sides
Angle sum =
=

(c) n = 10
∴ The sum of the angles of a polygon of 10 sides
Angle sum =
=

(d) Clearly from the given table it is observed that the number of triangles is two less them the number of sides in the polygon.
∴ If the polygon has n sides, the number of triangles formed will be (n – 2).
Since the sum of angles of a triangle = 180°
∴ The sum of angles of a polygon of n sides = (n – 2) x 180°.

Ex 3.1 Class 8 Maths Question 5.
What is a regular polygon? State the name of a regular polygon of
(i) 3 slides
(ii) 4 slides
(iii) 6 slides
Solution.
A polygon is said to be a regular polygon, if all its

1. interior angles are equal;
2. sides are equal; and
3. exterior angles are euqal.

The name of a regular polygon of

1. 3 sides is equilateral triangle.
2. 4 sides is square.
3. 6 sides is regular hexagon.

Ex 3.1 Class 8 Maths Question 6.
Find the angle measure x in the following figures.

Solution.

Ex 3.1 Class 8 Maths Question 7.

(a) Find x + y + z
(b) Find x + y + z + w.
Solution.

 

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