Maharashtra Board Class 6 Maths part 1 Chapter 2 Angles PDF Download

Angles

Let's Recall

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:

Teacher's Note

An angle is made by two rays that meet at a point. You see angles everywhere in your school, home, and even in your food items.

Exam Trick

Remember: The point where two lines meet is called the vertex. The two lines are called arms. Angle = Vertex + Two Arms.

Points to Remember

An angle has two arms and one vertex.
The vertex is the point where the two arms meet.
Angles are all around us in everyday life.

Try This

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.

Teacher's Note

This activity helps children understand angles using their bodies. It is like the angles made by a clock's hands at different times.

Exam Trick

Use your body as a tool to remember angles. Stand with your arms and move them to show different angles.

Points to Remember

Children can make angles using ropes.
Movement helps us understand angles better.
Straight lines are important to make angles.

Types of Angles

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 an acute angle.

An angle greater than 0° but less than 90° is called an acute angle.

The angle formed in figure (c) is a right angle.

An angle of 90° is called a right angle.

The angle formed in figure (d) is an obtuse angle.

An angle greater than 90° but less than 180° is called an obtuse 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°.

Teacher's Note

Show children a clock. The angle between the hands changes throughout the day. At 3 o'clock, the angle is a right angle (90°).

Exam Trick

Remember using "OARSR": Obtuse is Open, Acute is Arrow-like, Right is 90°, Straight is 180°, Reflex is Really big.

Points to Remember

Zero angle = 0°
Acute angle = between 0° and 90°
Right angle = 90°
Obtuse angle = between 90° and 180°
Straight angle = 180°
Reflex angle = between 180° and 360°
Complete angle = 360°

Try This

Use two sticks of different colours to make the angles from angle (a) to angle (g).

Teacher's Note

Using coloured sticks makes it easy for children to see the difference between angles. You can use pencils or straws instead of sticks.

Exam Trick

Draw and label all angle types in your notebook. Write the degree measure next to each one for quick review before the exam.

Points to Remember

Different colours help us see angles better.
All angles have a vertex and two arms.
The size of the angle depends on how far apart the arms are.

Practice Set 2

Look at the pictures above and identify the different types of angles.

1. Match the following

Measure of the angle: (1) 180°, (2) 240°, (3) 360°, (4) 0°

Type of angle: (a) Zero angle, (b) Straight angle, (c) Reflex angle, (d) Complete angle

2. The measures of some angles are given below. Write the type of each angle.

(1) 75°

(2) 0°

(3) 215°

(4) 360°

(5) 180°

(6) 120°

(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.

Teacher's Note

A protractor is a tool that measures angles. Every student should practise using it. It looks like a half circle with numbers.

Exam Trick

Remember: Protractor has numbers from 0 to 180. Always keep the middle point on the vertex of the angle.

Points to Remember

A protractor measures angles in degrees.
The middle hole of the protractor goes on the vertex.
We can draw angles using a protractor and ruler.
Acute angles are less than 90°.
Right angles are exactly 90°.

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