NCERT Solutions for Class 6 Maths

NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes Ex 5.5 are part of NCERT Solutions for Class 6 Maths. Here we have given NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes Ex 5.5.

• Understanding Elementary Shapes Class 6 Ex 5.1
• Understanding Elementary Shapes Class 6 Ex 5.2
• Understanding Elementary Shapes Class 6 Ex 5.3
• Understanding Elementary Shapes Class 6 Ex 5.4
• Understanding Elementary Shapes Class 6 Ex 5.6
• Understanding Elementary Shapes Class 6 Ex 5.7
• Understanding Elementary Shapes Class 6 Ex 5.8
• Understanding Elementary Shapes Class 6 Ex 5.9

NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes Ex 5.5

Question 1.
Which of the following are models for perpendicular lines :
(a) The adjacent edges of a table top.
(b) The lines of a railway track.
(c) The line segments forming the letter “L”.
(d) The letter V.
Solution :
(a) and (c) are models for perpendicular lines.

Question 2.
Let \(\overline { PQ }\) be the perpendicular to the line segment \(\overline { XY }\) . Let \(\vec { PQ }\) and \(\overline { XY }\) intersect in the point A. What is the measure of ∠PAY ?
Solution :
The measure of ∠PAY is 90°.

Question 3.
There are two “set-squares ” in your box. What are the measures of the angles that are formed at their comers? Do they have any angle measure that is common?
Solution :
One is a 30° – 60° – 90° set square; the other is a 45° – 45° – 90° set square. The angle of measure 90° (i.e., a right angle) is common between them.

Question 4.
Study the diagram. The line l is perpendicular to line m.

(a) Is CE = EG?
(b) Does PE bisect CG?
(c) Identify any two line segments for which PE is the perpendicular bisector.
(d) Are these true?
(i) AC > EG
(ii) CD = GH
(iii) BC < EH.
Solution :
(a) CE= CD + DE
= 1 + 1=2 units
EG = EF + FG
= 1 + 1=2 units
∴ CE= EG

(b) ∴ CE = EG
∴ E is the mid-point of CG.
∴ Line PE bisects line segment CG

(c) ∴ DE = EF = 1 unit
∴ PE is the perpendicular bisector of line segment DF
∴ BE = EH = 3 units
∴ PE is the perpendicular bisector of BH

(d)
(i) true
(ii) true
(iii) true

We hope the NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes Ex 5.5 help you. If you have any query regarding NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes Ex 5.5, drop a comment below and we will get back to you at the earliest.

NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes Ex 5.4 are part of NCERT Solutions for Class 6 Maths. Here we have given NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes Ex 5.4.

• Understanding Elementary Shapes Class 6 Ex 5.1
• Understanding Elementary Shapes Class 6 Ex 5.2
• Understanding Elementary Shapes Class 6 Ex 5.3
• Understanding Elementary Shapes Class 6 Ex 5.5
• Understanding Elementary Shapes Class 6 Ex 5.6
• Understanding Elementary Shapes Class 6 Ex 5.7
• Understanding Elementary Shapes Class 6 Ex 5.8
• Understanding Elementary Shapes Class 6 Ex 5.9

NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes Ex 5.4

Question 1.
What is the measure of
(i) a right angle
(ii) a straight angle?
Solution :
(i) The measure of a right angle is 90°.
(ii) The measure of a straight angle is 180°.

Question 2.
Say True or False:
(a) The measure of an acute angle < 90°.
(b) The measure of an obtuse angle of < 90°.
(c) The measure of reflex angle > 180°.
(d) The measure of one complete revolution = 360°.
(e) If m∠A = 53° and m∠B = 35°, then m∠A > m∠B.
Solution :
(a) True
(b) False
(c) True
(d) True
(e) True.

Question 3.
Write down the measures of
(a) some acute angles.
(b) some obtuse angles. (give at least two examples of each).
Solution :
(a) 23°, 89°
(b) 91°, 179°.

Question 4.
Measure the angles given below, using the Protractor and write down the measure.

Solution :
(a) 45°
(b) 125°
(e) 90°
(d) ∠l = 40°, ∠2 = 125° and ∠3 = 95°.

Question 5.
Which angle has a large measure? First, estimate and then measure.

Measure of angle A =
Measure of angle B =
Solution :
Measure of angle A = 40°
Measure of angle B = 65°
The angle B has a larger measure.

Question 6.
From these two angles which have larger measure? Estimate and then confirmed by the measuring them.

Solution :
Measure of first angle = 45°
Measure of second angle = 60°
The second angle has larger measure.

Question 7.
Fill in the blanks with acute, obtuse, right or straight:
(a) An angle whose measure is less than that of a right angle is. ____________
(b) An angle whose measure is greater than that of a right angle is. ____________
(c) An angle whose measure is the sum of the measures of two right angles is. ____________
(d) When the sum of the measures of two angles is that of a right angle, then each one of them is. ____________
(e) When the sum of the measures of two angles is that of a straight angle and if one of them is acute than the other should be ____________.
Solution :
(a) An angle whose measure is less than that of a right angle is an acute angle.
(b) An angle whose measure is greater than that of a right angle is the obtuse angle (if the angle is less than 180°)
(c) An angle whose measure is the sum of the measures of two right angles is the straight angle.
(d) When the sum of the measures of two angles is that of a right angle, then each one of them is acute.
(e) When the sum of the measures of two angles is that of a straight angle and if one of them is acute than the other should be an obtuse angle.

Question 8.
Find the measure of the angle shown in each figure. (First, estimate with your eye, and then find the actual measurements with a protractor).
(a)

(b)

(c)

(d)

Solution :
Estimation with eye
(a) 45°
(b) 125°
(c) 60°
(d) 135° actual measure with a protractor
Solution :
(a) 40°
(b) 130°
(c) 65°
(d) 135°

Question 9.
Find the angle measure between the hands of the clock in each figure :

Solution :

• 90°
• 30°
• 180°.

Question 10.
Investigate :

In the given figure, the angle measures 30°. Look at the same figure through a magnifying glass. Does the angle become larger? Does the size of the angle change?
Solution :
No!; No!

Question 11.
Measure and classify each angle :

Solution :
Angle ∠AOB ∠AOC ∠BOC ∠DOC ∠DOA ∠DOB Measure 40° 120° 80° 105° 140° 180° Type acute obtuse acute obtuse straight.

We hope the NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes Ex 5.4 help you. If you have any query regarding NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes Ex 5.4, drop a comment below and we will get back to you at the earliest.

NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes Ex 5.3 are part of NCERT Solutions for Class 6 Maths. Here we have given NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes Ex 5.3.

• Understanding Elementary Shapes Class 6 Ex 5.1
• Understanding Elementary Shapes Class 6 Ex 5.2
• Understanding Elementary Shapes Class 6 Ex 5.4
• Understanding Elementary Shapes Class 6 Ex 5.5
• Understanding Elementary Shapes Class 6 Ex 5.6
• Understanding Elementary Shapes Class 6 Ex 5.7
• Understanding Elementary Shapes Class 6 Ex 5.8
• Understanding Elementary Shapes Class 6 Ex 5.9

NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes Ex 5.3

Question 1.
Match the following :
(i) Straight angle (a) Less than one-fourth a revolution.
(ii) Right angle    (b) More than half a revolution
(iii) Acute angle   (c) Half of a revolution
(iv) Obtuse angle (d) One-fourth a revolution
(v) Reflex angle    (e) Between \(\frac { 1 }{ 4 }\) and \(\frac { 1 }{ 2 }\) of a revolution (f) One complete revolution.
Solution :
(i) Straight angle ↔ (c) Half of a revolution
(ii) Right angle ↔ (d) One-fourth a revolution
(iii) Acute angle ↔ (a) Less than one-fourth a revolution
(iv) Obtuse angle ↔ (e) Between 1/4 and 1/2 of a revolution
(v) Reflex angle ↔ (b) More than half a revolution.

Question 2.
Classify each one of the following angles as right, straight, acute, obtuse or reflex :

Solution :
(a) Acute
(b) Obtuse
(c) Right
(d) Reflex
(e) Straight
(f) Acute.

We hope the NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes Ex 5.3 help you. If you have any query regarding NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes Ex 5.3, drop a comment below and we will get back to you at the earliest.

NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes Ex 5.2 are part of NCERT Solutions for Class 6 Maths. Here we have given NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes Ex 5.2.

• Understanding Elementary Shapes Class 6 Ex 5.1
• Understanding Elementary Shapes Class 6 Ex 5.3
• Understanding Elementary Shapes Class 6 Ex 5.4
• Understanding Elementary Shapes Class 6 Ex 5.5
• Understanding Elementary Shapes Class 6 Ex 5.6
• Understanding Elementary Shapes Class 6 Ex 5.7
• Understanding Elementary Shapes Class 6 Ex 5.8
• Understanding Elementary Shapes Class 6 Ex 5.9

NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes Ex 5.2

Question 1.
What fraction of a clockwise revolution does the hour hand of a clock turn through, when it goes from
(a) 3 to 9
(b) 4 to 7
(c) 7 to 10
(d) 12 to 9
(e) 1 to 10
(f) 6 to 3?
Solution :
(a) \(\frac { 1 }{ 2 }\) of a revolution
(b) \(\frac { 1 }{ 4 }\) of a revolution
(c) \(\frac { 1 }{ 4 }\) of a revolution
(d) \(\frac { 3 }{ 4 }\) of a revolution
(e) \(\frac { 3 }{ 4 }\) of a revolution
(f) \(\frac { 3 }{ 4 }\) of a revolution.

Question 2.
Where will the hand of a clock stop, if it
(a) starts at 12 and makes 1/2 of a revolution, clockwise?
(b) starts at 2 and makes 1/2 of a revolution, clockwise?
(c) starts at 5 and makes 1/4 of a revolution, clockwise?
(d) starts at 5 and makes 3/4 of a revolution, clockwise?
Solution :
(a) at 6
(b) at 8
(c) at 8
(d) at 2.

Question 3.
Which direction will you face if you start facing
(a) east and make 1/2 of a revolution clockwise?
(b) east and make 1/2 of a revolution clockwise?
(c) west and make 3/4 of a. revolution anti-clockwise?
(d) south and make one full revolution? (Should we specify clockwise or anti-clockwise for this last question? Why not?)
Solution :
(a) West
(b) West
(c) North
(d) South.
To answer (d), it is immaterial whether we turn clockwise or anti-clockwise because one full revolution will bring us back to the original position.

Question 4.
What part of a revolution have you turned through if you stand to face
(a) east and turn clockwise to face north?
(b) south and turn clockwise to face east?
(c) west and turn clockwise to face east?
Solution :
(a) \(\frac { 3 }{ 4 }\) of a revolution.
(b) \(\frac { 3 }{ 4 }\) of a revolution.
(c) \(\frac { 1 }{ 2 }\) of a revolution.

Question 5.
Find the number of right angles turned through by the hour hand of a clock when it goes from
(a) 3 to 6
(b) 2 to 8
(c) 5 to 11
(d) 10 to 1
(e) 12 to 9
(f) 12 to 9
Solution :
(a) 1 right angle
(b) 2 right angles
(c) 2 right angles
(d) 1 right angle
(e) 3 right angles
(f) 2 right angle

Question 6.
Now many right angles do you make if you start facing
(a) south and turn clockwise to the west?
(b) north and turn anti-clockwise to the east?
(c) west and turn to west?
(d) south and turn to the north?
Solution :
(a) 1 right angle
(b) 3 right angles
(c) 4 right angles
(d) 2 right angles
(clockwise or anticlockwise).

Question 7.
Where will the hour’s hand of a clock stop if it starts
(a) from 6 and turns through 1 right angle?
(b) from 8 and turns through 2 right angles?
(c) from 10 and turns through 3 right angles?
(d) from 7and turns through 2 straight angles?
Solution :
(a) 9
(b) 2
(c) 7
(d) 7.
(We should consider only clockwise direction here).

We hope the NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes Ex 5.2 help you. If you have any query regarding NCERT Solutions for Class 6 Maths Chapter 5 Understanding Elementary Shapes Ex 5.2, drop a comment below and we will get back to you at the earliest.

NCERT Solutions for Class 6 Maths Chapter 3 Playing With Numbers Ex 3.2 are part of NCERT Solutions for Class 6 Maths. Here we have given NCERT Solutions for Class 6 Maths Chapter 3 Playing With Numbers Ex 3.2.

• Playing With Numbers Class 6 Ex 3.1
• Playing With Numbers Class 6 Ex 3.3
• Playing With Numbers Class 6 Ex 3.4
• Playing With Numbers Class 6 Ex 3.5
• Playing With Numbers Class 6 Ex 3.6
• Playing With Numbers Class 6 Ex 3.7

NCERT Solutions for Class 6 Maths Chapter 3 Playing With Numbers Ex 3.2

Question 1.
What is the sum of any two :
(a) Odd numbers
(b) Even numbers.
Solution :
(a) The sum of any two odd numbers is an even number.
(b) The sum of any two even numbers is an even number.

Question 2.
State whether the following statements are True or False :

1. The sum of three odd numbers is even.
2. The sum of two odd numbers and one even number is even.
3. The product of three odd numbers is odd.
4. If an even number is divided by 2, the quotient is always odd.
5. All prime numbers are odd.
6. Prime numbers do not have any factors.
7. Sum of two prime numbers is always even.
8. 2 is the only even prime number.
9. All even numbers are composite numbers.
10. The product of two even numbers is always even.

Solution :

1. This statement is false.
2. This statement is true.
3. This statement is true.
4. This statement is false.
5. This statement is false.
6. This statement is false.
7. This statement is false.
8. This statement is true.
9. This statement is false.
10. This statement is true.

Question 3.
The numbers 13 and 31 are prime numbers. Both these numbers have the same digits 1 and 3. Find such pairs of prime numbers up to 100.
Solution :
All other such pairs of prime numbers up to 100 are as follows :
17 and 71; 37 and 73; 79 and 97.

Question 4.
Write down separately the prime and composite numbers less than 20.
Solution :

Question 5.
What is the greatest prime number between 1 and 10?
Solution :
The greatest prime number between 1 and 10 is 7.

Question 6.
Express the following as the sum of two odd primes :
(a) 44
(b) 36
(c) 24
(d) 18.
Solution :
(a) 44 = 3+41
(b) 36 = 5 + 31
(c) 24 = 5+19
(d) 18 = 5+13.

Question 7.
Give three pairs of prime numbers whose difference is 2.
[Remark: Two prime numbers whose difference is 2 are called twin primes],
Solution :
The three pairs of prime numbers, whose difference is 2, are as follows :
3, 5 ; 5, 7 ; 11, 13.

Question 8.
Which of the following numbers are prime?
(a) 23
(b) 51
(c) 37
(d) 26.
Solution :
(a) 23,
(c) 37 are prime numbers.

Question 9.
Write seven consecutive composite numbers less than 100 so that there is no prime number between them.
Solution :
90, 91, 92, 93, 94, 95, 96.

Question 10.
Express each of the following numbers as the sum of three odd primes :
(a) 21
(b) 31
(c) 53
(d) 61.
Solution :
(a) 21 = 3 + 5 + 13
(b) 31 = 3 + 5 + 23
(c) 53 = 13+ 17 + 23
(d) 61 =7;+ 13+41.

Question 11.
Write five pairs of prime numbers below 20 whose sum is divisible by 5. (Hint: 3 + 7 – 10).
Solution :
2, 3 ; 2, 13 ; 3, 17 ; 7, 13 ; 11, 19.

Question 12.
Fill in the blanks in the following :

1. A number which has only two factors is called a
2. A number which has more than two factors is called a
3. 1 is neither nor
4. The smallest prime number is
5. The smallest composite number is
6. The smallest even number is

Solution :

1. A number which has only two factors is called a prime number.
2. A number which has more than two factors is called a composite number.
3. 1 is neither prime number nor composite number.
4. The smallest prime number is 2.
5. The smallest composite number is 4.
6. The smallest even number is 2.

We hope the NCERT Solutions for Class 6 Maths Chapter 3 Playing With Numbers Ex 3.2 help you. If you have any query regarding NCERT Solutions for Class 6 Maths Chapter 3 Playing With Numbers Ex 3.2, drop a comment below and we will get back to you at the earliest.