In this page we have *NCERT Solutions for Class 8 Maths Chapter 3 : Understanding quadrilaterals* for
EXERCISE 3.1 . Hope you like them and do not forget to like , social share
and comment at the end of the page.

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

(b) 1, 2, 5, 6, 7

(c) 1, 2

(d) 2

(e) 1

How many diagonals does each of the following have?

(a) A convex quadrilateral

(b) A regular hexagon

(c) A triangle

(a) There are 2 diagonals in a convex quadrilateral.

(b) There are 9 diagonals in a regular hexagon.

(c) A triangle does not have any diagonal in it.

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

The sum of the measures of the angles of a convex quadrilateral is 360° as a convex quadrilateral is made of two triangles.

In above convex quadrilateral, it made of two triangles. Therefore, the sum of all the interior angles of this quadrilateral will be same as the sum of all the interior angles of these two triangles i.e., 180º + 180º = 360º

This property also holds true for a quadrilateral which is not convex. This is because any quadrilateral can be divided into two triangles.

Here again, above concave quadrilateral is made of two triangles. Therefore, sum of all the interior angles of this quadrilateral will also be 180º + 180º = 360º

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)

From the table, it can be observed that the angle sum of a convex polygon of

So the angle sum of the convex polygons having number of sides as above will be as follows.

(a) (7 − 2) × 180º = 900°

(b) (8 − 2) × 180º = 1080°

(c) (10 − 2) × 180º = 1440°

(d) (

What is a regular polygon?

State the name of a regular polygon of

(i) 3 sides

(ii) 4 sides

(iii) 6 sides

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

(i) Equilateral Triangle

(ii) Square

(iii) Regular Hexagon

Find the angle measure

(a)

Sum of the measures of all interior angles of a quadrilateral is 360°. Therefore, in the given quadrilateral,

50° + 130° + 120° +

300° +

(b)

Let the other unknown angle be p,then 90 and p forms a linear pair

90º +

Sum of the measures of all interior angles of a quadrilateral is 360º. Therefore, in the given quadrilateral,

60° + 70° +

220° +

(c)

Let the other unknown angle be p and q in the pentagon,

then

70 +

60° +

Sum of the measures of all interior angles of a pentagon is

=540º.

Therefore, in the given pentagon,

120° + 110° + 30° +

260° + 2

2

(d)

Sum of the measures of all interior angles of a pentagon is 540º.

5

(a)find $x + y + z$

(b)find $x + y + z+w$

(a) x+ 90° = 180° (Linear pair)

x= 90°

z+ 30° = 180° (Linear pair)

z= 150°

y= 90° + 30° (Exterior angle theorem)

y= 120°

x + y + z= 90° + 120° + 150° = 360°

(b)

Sum of the measures of all interior angles of a quadrilateral is 360º. Therefore, in the given quadrilateral,

a+ 60° + 80° + 120° = 360°

a+ 260° = 360°

a= 100°

x+ 120° = 180° (Linear pair)

x= 60°

y+ 80° = 180° (Linear pair)

y= 100°

z+ 60° = 180° (Linear pair)

z= 120°

w+ 100° = 180° (Linear pair)

w= 80°

Sum of the measures of all interior angles =x + y + z + w

= 60° + 100° + 120° + 80°

= 360°

Download Chapter 3 Exercise 3.1 as pdf

**Notes****NCERT Solutions**

Class 8 Maths Class 8 Science