NCERT Solutions for Class 6 Maths Chapter 5 (Ex 5.4)
Exercise 5.4
What is the measure of the following angles?
A right angle
Ans: A right angle is that angle that is formed between two perpendicular lines. We know that the perpendicular lines form an angle of $90^\circ $.
Therefore, the measure of a right angle is $90^\circ $.
A right angle is indicated in the figure below.
A straight angle
Ans: A straight angle is that angle that is formed over a straight line. We know that the measure of an angle over a straight line is $180^\circ $.
Therefore, the measure of a straight angle is $180^\circ $.
A straight angle is indicated in the figure below.
Say whether true or false:
The measure of an acute angle is $ < 90^\circ $.
Ans: An acute angle is an angle that measures less than $90^\circ $. In other words, an acute angle lies between $0^\circ $ to $90^\circ $.
We can also say that the measure of the acute angle lies between zero angle and a right angle.
The given statement says that the measure of an acute angle is $ < 90^\circ $.
Therefore, by using the definition of an acute angle, the given statement is true.
The measure of an obtuse angle is $ < 90^\circ $.
Ans: An obtuse angle is an angle that measures more than $90^\circ $. In other words, an obtuse angle lies between $90^\circ $ to $180^\circ $.
We can also say that the measure of the obtuse angle lies between right angle and a straight angle.
The given statement says that the measure of an obtuse angle is $ < 90^\circ $.
Therefore, by using the definition of an obtuse angle, the given statement is false.
The measure of a reflex angle is$ > 180^\circ $.
Ans: A reflex angle is an angle that measures more than $180^\circ $. In other words, a reflex angle lies between $180^\circ $ to $360^\circ $.
We can also say that the measure of the reflex angle lies between straight angle and a complete angle.
The given statement says that the measure of a reflex angle is $ > 180^\circ $.
Therefore, by using the definition of a reflex angle, the given statement is true.
The measure of one complete revolution is $ = 360^\circ $.
Ans: The measure of a complete revolution is $360^\circ $. The angle having a measure of $360^\circ $ is known as the complete angle or Perigon.
Moreover, the measure of a circle is also $360^\circ $.
The given statement says that the measure of one complete revolution is $ = 360^\circ $.
Therefore, by using the definition of a complete angle, the given statement is true.
If $m\angle A = 53^\circ $ and $m\angle B = 35^\circ $, then $m\angle A > m\angle B$.
Ans: The measure of angles is determined by its magnitude. The larger angles have larger measures whereas smaller angles have smaller measures.
The given statement says that if $m\angle A = 53^\circ $ and $m\angle B = 35^\circ $, then $m\angle A > m\angle B$.
Now we know that in terms of magnitude,
$53^\circ > 35^\circ $
Hence, $m\angle A > m\angle B$
Therefore, the given statement is true.
Write down the measures of:
Some acute angles Give at least two examples of each.
Ans: An acute angle is an angle that measures less than $90^\circ $. In other words, an acute angle lies between $0^\circ $ to $90^\circ $.
We can also say that the measure of the acute angle lies between zero angle and a right angle.
Some examples of acute angles are $70^\circ $, $20^\circ $, $35^\circ $, $87^\circ $, and $11^\circ $.
Some obtuse angles Give at least two examples of each.
Ans: An obtuse angle is an angle that measures more than $90^\circ $. In other words, an obtuse angle lies between $90^\circ $ to $180^\circ $.
We can also say that the measure of the obtuse angle lies between the right angle and a straight angle.
Some examples of obtuse angles are $110^\circ $, $167^\circ $, $135^\circ $, $146^\circ $, and $174^\circ $.
Measure the angles given below, using the protractor and write down the measure:
Ans: An angle is formed when two rays intersect.
An angle is measured with the help of a protractor.
To measure the given angle, label the vertex and the arms of the angle as follows,
Place the centre of the protractor at the vertex of the angle, i.e., point $B$. Then place the line marking the $0^\circ $ angle over the arm $AB$. The line on the protractor that overlaps the arms $BC$, will give the measure of the angle.
On measuring with a protractor, the measure of the given angle is found to be $40^\circ $.
Ans: An angle is formed when two rays intersect.
An angle is measured with the help of a protractor.
To measure the given angle, label the vertex and the arms of the angle as follows,
Place the centre of the protractor at the vertex of the angle, i.e., point $B$. Then place the line marking the $0^\circ $ angle over the arm $AB$. The line on the protractor that overlaps the arms $BC$, will give the measure of the angle.
On measuring with a protractor, the measure of the given angle is found to be $130^\circ $.
Ans: An angle is formed when two rays intersect.
An angle is measured with the help of a protractor.
To measure the given angle, label the vertex and the arms of the angle as follows,
Place the centre of the protractor at the vertex of the angle, i.e., point $B$. Then place the line marking the $0^\circ $ angle over the arm $AB$. The line on the protractor that overlaps the arms $BC$, will give the measure of the angle.
On measuring with a protractor, the measure of the given angle is found to be $90^\circ $.
Ans: An angle is formed when two rays intersect.
An angle is measured with the help of a protractor.
To measure the given angle, label the vertex and the arms of the angle as follows,
Place the centre of the protractor at the vertex of the angle, i.e., point $B$. Then place the line marking the $0^\circ $ angle over the arm $AB$. The line on the protractor that overlaps the arms $BC$, will give the measure of the angle.
On measuring with a protractor, the measure of the given angle is found to be $60^\circ $.
Place the centre of the protractor at the vertex of the angle, i.e., point $D$. Then place the line marking the $0^\circ $ angle over the arm $AD$. The line on the protractor that overlaps the arms $DE$, will give the measure of the angle.
On measuring with a protractor, the measure of the given angle is found to be $130^\circ $.
Place the centre of the protractor at the vertex of the angle, i.e., point $E$. Then place the line marking the $0^\circ $ angle over the arm $EF$. The line on the protractor that overlaps the arms $ED$, will give the measure of the angle.
On measuring with a protractor, the measure of the given angle is found to be $90^\circ $.
Which angle has a large measure? First estimate and then measure.
Measure of angle $A = $
Measure of angle $B = $
Ans: An angle is formed when two rays intersect.
An angle is measured with the help of a protractor.
It is required to estimate which angle has a larger measure. The angles whose arms are wider have more measures as compared to the angles whose arms are narrower or closer to each other.
From the given figure, it is seen clearly that the arms of $\angle B$ are wider as compared to the arms of $\angle A$.
Therefore, $\angle B$ will have a larger measure as compared to $\angle A$.
It is also required to measure the given angles.
We will first measure $\angle A$.
To measure the given angle, label the vertex and the arms of the angle as follows,
Place the centre of the protractor at the vertex of the angle, i.e., point $A$. Then place the line marking the $0^\circ $ angle over the arm $AY$. The line on the protractor that overlaps the arms $AX$, will give the measure of the angle.
On measuring with a protractor, the measure of the given angle is found to be $40^\circ $.
We will now measure $\angle B$.
To measure the given angle, label the vertex and the arms of the angle as follows
Place the centre of the protractor at the vertex of the angle, i.e., point $B$. Then place the line marking the $0^\circ $ angle over the arm $BP$. The line on the protractor that overlaps the arms $BQ$, will give the measure of the angle.
On measuring with a protractor, the measure of the given angle is found to be $65^\circ $.
Therefore, we can conclude that $\angle B$is larger than $\angle A$. Also, the measure of $\angle A$ is $40^\circ $ and the measure of $\angle B$ is $65^\circ $.
From these two angles which has larger measure? Estimate and then confirm by measuring them:
Ans: An angle is formed when two rays intersect.
An angle is measured with the help of a protractor.
It is required to estimate which angle has a larger measure. To do so, label the vertices of both the angles for identification purposes.
The angles whose arms are wider have more measures as compared to the angles whose arms are narrower or closer to each other.
From the given figure, it is seen clearly that the arms of $\angle B$ are wider as compared to the arms of $\angle A$.
Therefore, $\angle B$ will have a larger measure as compared to $\angle A$.
It is also required to measure the given angles.
We will first measure $\angle A$.
To measure the given angle, label the vertex and the arms of the angle as follows,
Place the centre of the protractor at the vertex of the angle, i.e., point $A$. Then place the line marking the $0^\circ $ angle over the arm $AY$. The line on the protractor that overlaps the arms $AX$, will give the measure of the angle.
On measuring with a protractor, the measure of the given angle is found to be $45^\circ $.
We will now measure $\angle B$.
To measure the given angle, label the vertex and the arms of the angle as follows,
Place the centre of the protractor at the vertex of the angle, i.e., point $B$. Then place the line marking the $0^\circ$ angle over the arm $BP$. The line on the protractor that overlaps the arms $BQ$, will give the measure of the angle.
On measuring with a protractor, the measure of the given angle is found to be $55^\circ $.
Hence, it is confirmed on measurement also that the measure of $\angle B$ is more than the measure of $\angle A$.
Therefore, we can conclude that the measure of the second angle is greater.
Fill in the blanks with acute, obtuse, right or straight:
An angle whose measure is less than that of a right angle is __________.
Ans: An acute angle is an angle that measures less than $90^\circ $. In other words, an acute angle lies between $0^\circ $ to $90^\circ $.
We can also say that the measure of the acute angle lies between zero angle and a right angle.
Therefore, by using the definition of an acute angle, the given statement can be completed as,
An angle whose measure is less than that of a right angle is acute angle.
An angle whose measure is greater than that of a right angle is __________.
Ans: An obtuse angle is an angle that measures more than $90^\circ $. In other words, an obtuse angle lies between $90^\circ $ to $180^\circ $.
We can also say that the measure of the obtuse angle lies between the right angle and a straight angle.
Therefore, by using the definition of an obtuse angle, the given statement can be completed as,
An angle whose measure is greater than that of a right angle is obtuse angle.
An angle whose measure is the sum of the measures of two right angles is __________.
Ans: A straight angle is that angle that is formed over a straight line. We know that the measure of an angle over a straight line is $180^\circ $.
Therefore, the measure of a straight angle is $180^\circ $.
A right angle is that angle that is formed between two perpendicular lines. We know that the perpendicular lines form an angle of $90^\circ $.
Therefore, the measure of a right angle is $90^\circ $.
Sum of two right angles will be equal to the measure of one straight angle.
Therefore, by using the definition of a straight angle, the given statement can be completed as,
An angle whose measure is the sum of the measures of two right angles is straight angle.
When the sum of the measures of two angles is that of a right angle, then each one of them is __________.
Ans: An acute angle is an angle that measures less than $90^\circ $. In other words, an acute angle lies between $0^\circ $ to $90^\circ $.
We can also say that the measure of the acute angle lies between zero angle and a right angle.
If two angles measure equal to a right angle, then each one of them must be smaller than the right angle.
Therefore, by using the definition of an acute angle, the given statement can be completed as,
When the sum of the measures of two angles is that of a right angle, then each one of them is acute angle.
When the sum of the measures of two angles is that of a straight angle and if one of them is acute then the other should be __________.
Ans: An obtuse angle is an angle that measures more than $90^\circ $. In other words, an obtuse angle lies between $90^\circ $ to $180^\circ $.
We can also say that the measure of the obtuse angle lies between the right angle and a straight angle.
If two angles measure equal to a straight angle such that one of them is acute, then this means that the measure of that angle is lesser than that of a right angle. So, the other angle will have to be greater than the right angle in order to form a straight line.
Therefore, by using the definition of an obtuse angle, the given statement can be completed as,
When the sum of the measures of two angles is that of a straight angle and if one of them is acute then the other should be an obtuse angle.
Find the measure of the angle shown in each figure. (First estimate with your eyes and then find the actual measure with a protractor).
Ans: An angle is formed when two rays intersect.
An angle is measured with the help of a protractor.
To measure the given angle, label the vertex and the arms of the angle as follows,
Place the centre of the protractor at the vertex of the angle, i.e., point $B$. Then place the line marking the $0^\circ $ angle over the arm $AB$. The line on the protractor that overlaps the arms $BC$, will give the measure of the angle.
On measuring with a protractor, the measure of the given angle is found to be $30^\circ $.
Ans: An angle is formed when two rays intersect.
An angle is measured with the help of a protractor.
To measure the given angle, label the vertex and the arms of the angle as follows,
Place the centre of the protractor at the vertex of the angle, i.e., point $B$. Then place the line marking the $0^\circ $ angle over the arm $AB$. The line on the protractor that overlaps the arms $BC$, will give the measure of the angle.
On measuring with a protractor, the measure of the given angle is found to be $120^\circ $.
Ans: An angle is formed when two rays intersect.
An angle is measured with the help of a protractor.
To measure the given angle, label the vertex and the arms of the angle as follows,
Place the centre of the protractor at the vertex of the angle, i.e., point $B$. Then place the line marking the $0^\circ $ angle over the arm $AB$. The line on the protractor that overlaps the arms $BC$, will give the measure of the angle.
On measuring with a protractor, the measure of the given angle is found to be $60^\circ $.
Ans: An angle is formed when two rays intersect.
An angle is measured with the help of a protractor.
To measure the given angle, label the vertex and the arms of the angle as follows,
Place the centre of the protractor at the vertex of the angle, i.e., point $B$. Then place the line marking the $0^\circ $ angle over the arm $AB$. The line on the protractor that overlaps the arms $BC$, will give the measure of the angle.
On measuring with a protractor, the measure of the given angle is found to be $150^\circ $.
Find the angle measure between the hands of the clock in each figure:
9:00 a.m.
Ans: An angle is formed when two rays intersect.
An angle is measured with the help of a protractor.
To measure the given angle, label the vertex and the arms of the angle as follows,
Place the centre of the protractor at the vertex of the angle, i.e., point $B$. Then place the line marking the $0^\circ $ angle over the arm $AB$. The line on the protractor that overlaps the arms $BC$, will give the measure of the angle.
On measuring with a protractor, the measure of the given angle is found to be $90^\circ $.
The given angle is a right angle. This is because a right angle is that angle which has a measure of $90^\circ $.
Therefore, the angle measure between the given hands of the clock is $90^\circ $.
1:00 p.m.
Ans: An angle is formed when two rays intersect.
An angle is measured with the help of a protractor.
To measure the given angle, label the vertex and the arms of the angle as follows,
Place the centre of the protractor at the vertex of the angle, i.e., point $B$. Then place the line marking the $0^\circ $ angle over the arm $AB$. The line on the protractor that overlaps the arms $BC$, will give the measure of the angle.
On measuring with a protractor, the measure of the given angle is found to be $30^\circ $.
The given angle is an acute angle. This is because an acute angle is that angle which has a measure of less than $90^\circ $.
Therefore, the angle measure between the given hands of the clock is $30^\circ $.
6:00 p.m.
Ans: An angle is formed when two rays intersect.
An angle is measured with the help of a protractor.
To measure the given angle, label the vertex and the arms of the angle as follows,
Place the centre of the protractor at the vertex of the angle, i.e., point $B$. Then place the line marking the $0^\circ $ angle over the arm $AB$. The line on the protractor that overlaps the arms $BC$, will give the measure of the angle.
On measuring with a protractor, the measure of the given angle is found to be $180^\circ $.
The given angle is a straight angle. This is because astraight angle is that angle which has a measure of $180^\circ $.
Therefore, the angle measure between the given hands of the clock is $180^\circ $.
Investigate:
In the given figure, the angle measure is$30^\circ $. Look at the same figure through a magnifying glass. Does the angle become larger? Does the size of the angle change?
Ans: An angle is formed when two rays intersect.
An angle is measured with the help of a protractor.
It is given that the measure of the angle in the given figure is $30^\circ $.
It is required to explain what happens when we observe the given angle with the help of a magnifying glass.
A magnifying glass is a tool that is used to enlarge anything which cannot be seen clearly with the help of naked eyes.
To do so, we will first take a magnifying glass and look at the given angle through it.
In doing so, we observe that the figure becomes larger. The angle also appears to become larger. However, the measure of the angle does not change. Only the size of the angle changes and it becomes bigger.
Measure and classify each angle:
Ans: An angle is formed when two rays intersect.
An angle is measured with the help of a protractor.
We will find the measure of each angle and then classify each angle based on the measure.
Consider $\angle AOB$.
Place the centre of the protractor at the vertex of the angle, i.e., point $O$. Then place the line marking the $0^\circ $ angle over the arm $OA$. The line on the protractor that overlaps the arms $OB$, will give the measure of the angle.
On measuring with a protractor, the measure of the given angle is found to be $40^\circ $.
The given angle is an acute angle. This is because an acute angle is that angle which has a measure of less than $90^\circ $.
Consider $\angle AOC$.
Place the centre of the protractor at the vertex of the angle, i.e., point $O$. Then place the line marking the $0^\circ $ angle over the arm $OA$. The line on the protractor that overlaps the arms $OC$, will give the measure of the angle.
On measuring with a protractor, the measure of the given angle is found to be $130^\circ $.
The given angle is an obtuse angle. This is because an obtuse angle is that angle that has a measure greater than $90^\circ $.
Consider $\angle BOC$.
Place the centre of the protractor at the vertex of the angle, i.e., point $O$. Then place the line marking the $0^\circ $ angle over the arm $OB$. The line on the protractor that overlaps the arms $OC$, will give the measure of the angle.
On measuring with a protractor, the measure of the given angle is found to be $90^\circ $.
The given angle is a right angle. This is because a right angle is that angle that has a measure of $90^\circ $.
Consider $\angle DOC$.
Place the centre of the protractor at the vertex of the angle, i.e., point $O$. Then place the line marking the $0^\circ $ angle over the arm $OC$. The line on the protractor that overlaps the arms $OD$, will give the measure of the angle.
On measuring with a protractor, the measure of the given angle is found to be $90^\circ $.
The given angle is a right angle. This is because a right angle is that angle which has a measure of $90^\circ $.
Consider $\angle DOA$.
Place the centre of the protractor at the vertex of the angle, i.e., point $O$. Then place the line marking the $0^\circ $ angle over the arm $OA$. The line on the protractor that overlaps the arms $OD$, will give the measure of the angle.
On measuring with a protractor, the measure of the given angle is found to be $140^\circ $.
The given angle is an obtuse angle. This is because an obtuse angle is that angle which has a measure greater than $90^\circ $.
Consider $\angle DOB$.
Place the centre of the protractor at the vertex of the angle, i.e., point $O$. Then place the line marking the $0^\circ $ angle over the arm $OB$. The line on the protractor that overlaps the arms $OD$, will give the measure of the angle.
On measuring with a protractor, the measure of the given angle is found to be $180^\circ $.
The given angle is a straight angle. This is because a straight angle is that angle that has a measure of $180^\circ $.
Therefore, the completed table is as follows,
NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes Exercise 5.4
Opting for the NCERT solutions for Ex 5.4 Class 6 Maths is considered as the best option for the CBSE students when it comes to exam preparation. This chapter consists of many exercises. Out of which we have provided the Exercise 5.4 Class 6 Maths NCERT solutions on this page in PDF format. You can download this solution as per your convenience or you can study it directly from our website/ app online.
Vedantu in-house subject matter experts have solved the problems/ questions from the exercise with the utmost care and by following all the guidelines by CBSE. Class 6 students who are thorough with all the concepts from the Maths textbook and quite well-versed with all the problems from the exercises given in it, then any student can easily score the highest possible marks in the final exam. With the help of this Class 6 Maths Chapter 5 Exercise 5.4 solutions, students can easily understand the pattern of questions that can be asked in the exam from this chapter and also learn the marks weightage of the chapter. So that they can prepare themselves accordingly for the final exam.
Besides these NCERT solutions for Class 6 Maths Chapter 5 Exercise 5.4, there are plenty of exercises in this chapter which contain innumerable questions as well. All these questions are solved/answered by our in-house subject experts as mentioned earlier. Hence all of these are bound to be of superior quality and anyone can refer to these during the time of exam preparation. In order to score the best possible marks in the class, it is really important to understand all the concepts of the textbooks and solve the problems from the exercises given next to it.
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