Textbook: Angles | Mathematics Class 6 (Maharashtra Board) PDF Download

 Page 1


6
  
Angles
 Look at the angles shown in the pictures below. Identify the type of angle and write its 
name below the picture.
............ ............ ............
Complete the following table :
Activity :  Ask three or more children to 
stand in a straight line. Take two long 
ropes. Let the child in the middle hold 
one end of each rope. With the help of 
the ropes, make the children on either 
side stand along a straight line. Tell them 
to move so as to form an acute angle, a 
right angle, an obtuse angle, a straight 
angle, a reflex angle and a full or complete 
angle in turn. Keeping the rope stretched 
will help to ensure that the children form 
straight lines.
2
Angles
P
R
Y
L
M
N
O
B
S
Angle
Name of the angle
Vertex of the angle
Arms of the angle
Let’s recall.
Try this.
Page 2


6
  
Angles
 Look at the angles shown in the pictures below. Identify the type of angle and write its 
name below the picture.
............ ............ ............
Complete the following table :
Activity :  Ask three or more children to 
stand in a straight line. Take two long 
ropes. Let the child in the middle hold 
one end of each rope. With the help of 
the ropes, make the children on either 
side stand along a straight line. Tell them 
to move so as to form an acute angle, a 
right angle, an obtuse angle, a straight 
angle, a reflex angle and a full or complete 
angle in turn. Keeping the rope stretched 
will help to ensure that the children form 
straight lines.
2
Angles
P
R
Y
L
M
N
O
B
S
Angle
Name of the angle
Vertex of the angle
Arms of the angle
Let’s recall.
Try this.
7
     
 :
In figure (a), the two sticks lie one upon the other. There 
is no change in their position. In this position, the angle 
between the sticks is called a zero angle. The measure of 
the zero angle is written as 0°.
Now, keeping one stick in place, turn the other one around 
as shown in the figure.
The angle formed in figure (b) is ..... .................. angle.
An angle greater than 0° but less than 90° is called .... 
.......... angle.
The angle formed in figure (c) is .... ............ angle.
An angle of 90° is called .... ............ angle.
The angle formed in figure (d) is ..... ............... angle.
An angle greater than 90° but less than 180° is called .... 
........... angle.
If the stick is turned further in the direction shown in figure 
(d) we get a position as in figure (e). An angle like this is 
called a straight angle. A straight angle measures 180°.
If the stick is turned even further as shown in figure (e), we 
get an angle like the one in figure (f). This angle is greater 
than 180°. Such an angle is called a reflex angle. A reflex 
angle is greater than 180° and less than 360°.
The stick in figure (f) completes one round and comes back 
to its original position as in figure (g). It turned through 180° 
till it made a straight angle and 180° after making the straight 
angle, thus completing 360° in all. An angle made in this 
way is called a full or complete angle. The measure of a 
complete angle is 360°.
(a)
(b)
(c)
(d)
(e)
(f)
(g)
Use two sticks of different colours to make the angles from                  
angle (a) to angle (g).
Try this.
Page 3


6
  
Angles
 Look at the angles shown in the pictures below. Identify the type of angle and write its 
name below the picture.
............ ............ ............
Complete the following table :
Activity :  Ask three or more children to 
stand in a straight line. Take two long 
ropes. Let the child in the middle hold 
one end of each rope. With the help of 
the ropes, make the children on either 
side stand along a straight line. Tell them 
to move so as to form an acute angle, a 
right angle, an obtuse angle, a straight 
angle, a reflex angle and a full or complete 
angle in turn. Keeping the rope stretched 
will help to ensure that the children form 
straight lines.
2
Angles
P
R
Y
L
M
N
O
B
S
Angle
Name of the angle
Vertex of the angle
Arms of the angle
Let’s recall.
Try this.
7
     
 :
In figure (a), the two sticks lie one upon the other. There 
is no change in their position. In this position, the angle 
between the sticks is called a zero angle. The measure of 
the zero angle is written as 0°.
Now, keeping one stick in place, turn the other one around 
as shown in the figure.
The angle formed in figure (b) is ..... .................. angle.
An angle greater than 0° but less than 90° is called .... 
.......... angle.
The angle formed in figure (c) is .... ............ angle.
An angle of 90° is called .... ............ angle.
The angle formed in figure (d) is ..... ............... angle.
An angle greater than 90° but less than 180° is called .... 
........... angle.
If the stick is turned further in the direction shown in figure 
(d) we get a position as in figure (e). An angle like this is 
called a straight angle. A straight angle measures 180°.
If the stick is turned even further as shown in figure (e), we 
get an angle like the one in figure (f). This angle is greater 
than 180°. Such an angle is called a reflex angle. A reflex 
angle is greater than 180° and less than 360°.
The stick in figure (f) completes one round and comes back 
to its original position as in figure (g). It turned through 180° 
till it made a straight angle and 180° after making the straight 
angle, thus completing 360° in all. An angle made in this 
way is called a full or complete angle. The measure of a 
complete angle is 360°.
(a)
(b)
(c)
(d)
(e)
(f)
(g)
Use two sticks of different colours to make the angles from                  
angle (a) to angle (g).
Try this.
8
(a) (b) (c)
(d)
(e)
(f)
 
 
 Look at the pictures above and identify the different types of angles.
1. Match the following. 2. The measures of some angles are given 
 Measure of      Type of angle  below. Write the type of each angle. 
 
the angle
     
 (1) 180° (a) Zero angle  (1) 75° (2) 0° 
 (2) 240° (b) Straight angle  (3) 215° (4) 360°  
 (3) 360° (c) Reflex angle  (5) 180° (6) 120°  
 (4) 0°  (d) Complete angle  (7) 148° (8) 90°    
3. Look at the figures below and write the type of each of the angles. 
4. Use a protractor to draw an acute angle, a right angle and an obtuse angle. 
Practice Set 2
 
My friend, Maths : At the fair, at home, in the garden.
Page 4


6
  
Angles
 Look at the angles shown in the pictures below. Identify the type of angle and write its 
name below the picture.
............ ............ ............
Complete the following table :
Activity :  Ask three or more children to 
stand in a straight line. Take two long 
ropes. Let the child in the middle hold 
one end of each rope. With the help of 
the ropes, make the children on either 
side stand along a straight line. Tell them 
to move so as to form an acute angle, a 
right angle, an obtuse angle, a straight 
angle, a reflex angle and a full or complete 
angle in turn. Keeping the rope stretched 
will help to ensure that the children form 
straight lines.
2
Angles
P
R
Y
L
M
N
O
B
S
Angle
Name of the angle
Vertex of the angle
Arms of the angle
Let’s recall.
Try this.
7
     
 :
In figure (a), the two sticks lie one upon the other. There 
is no change in their position. In this position, the angle 
between the sticks is called a zero angle. The measure of 
the zero angle is written as 0°.
Now, keeping one stick in place, turn the other one around 
as shown in the figure.
The angle formed in figure (b) is ..... .................. angle.
An angle greater than 0° but less than 90° is called .... 
.......... angle.
The angle formed in figure (c) is .... ............ angle.
An angle of 90° is called .... ............ angle.
The angle formed in figure (d) is ..... ............... angle.
An angle greater than 90° but less than 180° is called .... 
........... angle.
If the stick is turned further in the direction shown in figure 
(d) we get a position as in figure (e). An angle like this is 
called a straight angle. A straight angle measures 180°.
If the stick is turned even further as shown in figure (e), we 
get an angle like the one in figure (f). This angle is greater 
than 180°. Such an angle is called a reflex angle. A reflex 
angle is greater than 180° and less than 360°.
The stick in figure (f) completes one round and comes back 
to its original position as in figure (g). It turned through 180° 
till it made a straight angle and 180° after making the straight 
angle, thus completing 360° in all. An angle made in this 
way is called a full or complete angle. The measure of a 
complete angle is 360°.
(a)
(b)
(c)
(d)
(e)
(f)
(g)
Use two sticks of different colours to make the angles from                  
angle (a) to angle (g).
Try this.
8
(a) (b) (c)
(d)
(e)
(f)
 
 
 Look at the pictures above and identify the different types of angles.
1. Match the following. 2. The measures of some angles are given 
 Measure of      Type of angle  below. Write the type of each angle. 
 
the angle
     
 (1) 180° (a) Zero angle  (1) 75° (2) 0° 
 (2) 240° (b) Straight angle  (3) 215° (4) 360°  
 (3) 360° (c) Reflex angle  (5) 180° (6) 120°  
 (4) 0°  (d) Complete angle  (7) 148° (8) 90°    
3. Look at the figures below and write the type of each of the angles. 
4. Use a protractor to draw an acute angle, a right angle and an obtuse angle. 
Practice Set 2
 
My friend, Maths : At the fair, at home, in the garden.
9
Get to know your compass box.
You have learnt what these instruments are used for.
 
There are two more types of instruments in the compass box. Let’s see how to use them.
Set Squares           
The
 
Divider
The instrument shown 
alongside is the divider. 
It is used to measure the 
distance between two   
Look  at  the  two  set  squares in the box and points. To do so, a scale 
observe their angles. Try and see how they can  also has to be used along
be  used to draw angles of 90°, 30°, 60° and 45°. with the divider. 
An
 
Angle Bisector
 
Take a sheet of tracing paper. Draw an angle of any measure 
on it. Fold the paper so that the arms of the angle fall on each 
other. What does the fold do? Observe that the fold divides the 
angle into two equal parts. This fold is the bisector of the angle.
Take points A and B on the arms of the angle at equal distances 
from the vertex. Now take points C, P, T on the bisector of the 
angle. Measure the distance of each of these points from the 
points A and B. 
Note that each of the points on the bisector is equidistant from the points A and B.
A
C
P
T
B
Compass Protractor
Scale/Ruler 
Let’s recall.
Let’s learn.
Try this.
Page 5


6
  
Angles
 Look at the angles shown in the pictures below. Identify the type of angle and write its 
name below the picture.
............ ............ ............
Complete the following table :
Activity :  Ask three or more children to 
stand in a straight line. Take two long 
ropes. Let the child in the middle hold 
one end of each rope. With the help of 
the ropes, make the children on either 
side stand along a straight line. Tell them 
to move so as to form an acute angle, a 
right angle, an obtuse angle, a straight 
angle, a reflex angle and a full or complete 
angle in turn. Keeping the rope stretched 
will help to ensure that the children form 
straight lines.
2
Angles
P
R
Y
L
M
N
O
B
S
Angle
Name of the angle
Vertex of the angle
Arms of the angle
Let’s recall.
Try this.
7
     
 :
In figure (a), the two sticks lie one upon the other. There 
is no change in their position. In this position, the angle 
between the sticks is called a zero angle. The measure of 
the zero angle is written as 0°.
Now, keeping one stick in place, turn the other one around 
as shown in the figure.
The angle formed in figure (b) is ..... .................. angle.
An angle greater than 0° but less than 90° is called .... 
.......... angle.
The angle formed in figure (c) is .... ............ angle.
An angle of 90° is called .... ............ angle.
The angle formed in figure (d) is ..... ............... angle.
An angle greater than 90° but less than 180° is called .... 
........... angle.
If the stick is turned further in the direction shown in figure 
(d) we get a position as in figure (e). An angle like this is 
called a straight angle. A straight angle measures 180°.
If the stick is turned even further as shown in figure (e), we 
get an angle like the one in figure (f). This angle is greater 
than 180°. Such an angle is called a reflex angle. A reflex 
angle is greater than 180° and less than 360°.
The stick in figure (f) completes one round and comes back 
to its original position as in figure (g). It turned through 180° 
till it made a straight angle and 180° after making the straight 
angle, thus completing 360° in all. An angle made in this 
way is called a full or complete angle. The measure of a 
complete angle is 360°.
(a)
(b)
(c)
(d)
(e)
(f)
(g)
Use two sticks of different colours to make the angles from                  
angle (a) to angle (g).
Try this.
8
(a) (b) (c)
(d)
(e)
(f)
 
 
 Look at the pictures above and identify the different types of angles.
1. Match the following. 2. The measures of some angles are given 
 Measure of      Type of angle  below. Write the type of each angle. 
 
the angle
     
 (1) 180° (a) Zero angle  (1) 75° (2) 0° 
 (2) 240° (b) Straight angle  (3) 215° (4) 360°  
 (3) 360° (c) Reflex angle  (5) 180° (6) 120°  
 (4) 0°  (d) Complete angle  (7) 148° (8) 90°    
3. Look at the figures below and write the type of each of the angles. 
4. Use a protractor to draw an acute angle, a right angle and an obtuse angle. 
Practice Set 2
 
My friend, Maths : At the fair, at home, in the garden.
9
Get to know your compass box.
You have learnt what these instruments are used for.
 
There are two more types of instruments in the compass box. Let’s see how to use them.
Set Squares           
The
 
Divider
The instrument shown 
alongside is the divider. 
It is used to measure the 
distance between two   
Look  at  the  two  set  squares in the box and points. To do so, a scale 
observe their angles. Try and see how they can  also has to be used along
be  used to draw angles of 90°, 30°, 60° and 45°. with the divider. 
An
 
Angle Bisector
 
Take a sheet of tracing paper. Draw an angle of any measure 
on it. Fold the paper so that the arms of the angle fall on each 
other. What does the fold do? Observe that the fold divides the 
angle into two equal parts. This fold is the bisector of the angle.
Take points A and B on the arms of the angle at equal distances 
from the vertex. Now take points C, P, T on the bisector of the 
angle. Measure the distance of each of these points from the 
points A and B. 
Note that each of the points on the bisector is equidistant from the points A and B.
A
C
P
T
B
Compass Protractor
Scale/Ruler 
Let’s recall.
Let’s learn.
Try this.
10
A
B
Q
P
P
C
C Q
A
B
B
Q C
P
A
?? ?? ?? ?? ?? ?? Let us see how to use geometrical instruments to construct geometrical figures.
(1) To draw an angle bisector using a compass.
Example : Draw any angle ABC. Draw its bisector.
  
 ?? Draw an angle ?ABC of any measure.
 ?? Now place the point of a compass on point B and with 
any convenient distance draw an arc to cut rays BA 
and BC. Name the points of intersection as P and Q 
respectively.
 ?? Now, place the point of the compass at P and taking a 
convenient distance, draw an arc inside the angle. Using 
the same distance, draw another arc inside the angle 
from the point Q, to cut the previous arc. 
  
 ?? Name the point of intersection as point O. Now draw          
ray BO. Ray BO is the bisector of ?ABC. Measure 
?ABO and ?CBO.  
 ?? Are they of equal measure?
(2) To construct an angle equal in measure to a given angle, using a compass and ruler.
Example : Look at the given ?ABC in the figure alongside. Draw ?PQR equal in measure 
to ?ABC. 
		 ?? Draw ray QR. 
		 ?? Place the compass point at vertex B of ?ABC 
and taking a convenient distance, draw an arc 
to cut the rays BA and BC at points D and E 
respectively.
		 ?? Using the same distance again, place the 
compass point at point Q of ray QR and draw 
an arc. Let this arc cut the ray QR at T. 
		 ?? Now place the point of the compass at point 
E and open the compass to a distance equal 
to DE.
C
B
A
E
D
Q R T
O