Maharashtra Board Class 5 Maths Part One Chapter 6 Angles PDF Download

6. Angles

Revision

This is a right angle. This is an acute angle. This is an obtuse angle.

Look at the clocks given below. Write whether the hands make a right angle, an acute angle or an obtuse angle in the box below.

Components Of Angles, Naming An Angle

Teacher: Monu, what does the diagram given here show?

Monu: The diagram shows an angle. Sir, do angles have names?

Teacher: Yes, angles have names. Can you see the lines in the diagram? Tell me their names.

Monu: This diagram has two lines, BA and BC.

Teacher: Which is the common point between the two lines?

Monu: The common point is B.

Teacher: These two lines join together to form an angle. The common point B is called the 'vertex'. BA and BC are the 'arms' of the angle.

Monu: Then, Sir, what is the name of the angle?

Teacher: An angle is named by three letters. The letter in the middle represents the vertex of the angle.

Monu: That means, the name of the angle is ABC. Is that right?

Teacher: Yes. While naming the angle, we say 'angle ABC'.

Monu: Sir, instead of 'angle ABC', can we say 'angle CBA'?

Teacher's Note

Angles are all around us. Look at the corner of your classroom door. That corner makes a right angle. We name angles using three letters to show the two lines and their common meeting point.

Exam Trick

Remember: The middle letter is always the vertex. So angle ABC means the vertex is at B. If you see angle PQR, the vertex is at Q. Always pick the middle letter!

Points to Remember

An angle is made when two lines meet at a point.

The meeting point is called the vertex.

The two lines are called the arms of the angle.

We name an angle using three letters. The middle letter is the vertex.

We can write angle ABC as angle CBA. Both names are correct.

The Protractor

A protractor is used to measure an angle and also to draw an angle according to a given measure.

A protractor is semi-circular in shape.

The semi-circular edge of a protractor is divided into 180 equal parts. Each part is 'one degree'. 'One degree' is written as '1°'.

The divisions on a protractor, i.e., the degrees can be marked in two ways. The divisions 0, 10, 20, 30,…180 are marked anticlockwise or from right to left; the divisions 0, 10, 20, 30,…180 are also marked clockwise, or serially from left to right.

The centre of the circle of which the protractor is a half part, is called the centre of the protractor. A diameter of that circle is the baseline or line of reference of the protractor.

Teacher's Note

A protractor looks like a half-circle ruler. You use it to measure angles just like you use a ruler to measure length. The number marks on the protractor tell you how many degrees an angle is.

Exam Trick

Remember: A protractor has numbers on two sides. Always start counting from 0. If the arm is on the right side, count from the 0 on the right. If it is on the left, count from the 0 on the left. This stops confusion!

Points to Remember

A protractor is shaped like a half-circle.

It has 180 equal parts. Each part is called one degree (1°).

The protractor has numbers marked in two ways - from left and from right.

The middle point of the straight edge is called the centre.

The straight edge is called the baseline or line of reference.

Measuring Angles

Observe how to measure ∠ABC given alongside, using a protractor.

First, put the centre of the protractor on the vertex B of the angle. Place the baseline of the protractor exactly on arm BC. The arms of the angle do not reach the divisions on the protractor.

At such times, set the protractor aside and extend the arms of the angle.

Extending the arms of the angle does not change the measure of the angle.

The angle is measured starting from the zero on that side of the vertex on which the arm of the angle lies. Here, the arm BC is on the right of the vertex B. Therefore, count the divisions starting from the 0 on the right. See which mark falls on arm BA. Read the number on that mark. This number is the measure of the angle. The measure of ∠ABC is 40°.

We can measure the same ∠ABC by positioning the protractor differently.

First put the centre point of the protractor on vertex B of the angle. Align the baseline of the protractor with arm BA.

Find the 0 mark on the side of BA. Count the marks starting from the 0 on the side of point A. See which mark falls on arm BC. Read the number at that point.

Observe that here, too, the measure of ∠ABC is 40°.

Teacher's Note

When you measure an angle, you can place the protractor in different ways. The important thing is to always start from 0 and count to where the other arm falls. Just like measuring your height with a measuring tape, the angle measurement will be the same no matter which direction you measure from.

Exam Trick

Remember: Always find the 0 mark first. Then count from 0 to where the second arm touches the protractor. Do not mix the two scales on the protractor. Pick one side and stick to it. If you start from the 0 on the right, keep using the right side only.

Points to Remember

Put the centre of the protractor on the vertex of the angle.

Place the baseline on one arm of the angle.

Start counting from 0 on the side where the arm lies.

Read the number where the other arm crosses the protractor.

If the arms are too short, you can extend them. This does not change the angle measure.

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