RS Aggrawal 2020 2021 Solutions for Class 6 Maths Chapter 13 Angles And Their Measurement are provided here with simple step-by-step explanations. These solutions for Angles And Their Measurement are extremely popular among class 6 students for Maths Angles And Their Measurement Solutions come handy for quickly completing your homework and preparing for exams. All questions and answers from the RS Aggrawal 2020 2021 Book of class 6 Maths Chapter 13 are provided here for you for free. You will also love the ad-free experience on Meritnationâ€™s RS Aggrawal 2020 2021 Solutions. All RS Aggrawal 2020 2021 Solutions for class 6 Maths are prepared by experts and are 100% accurate.

#### Page No 176:

#### Question 1:

#### Answer:

Three examples from our daily life are as follows:

1) Angle formed at the vertex of our elbow with the upper arm and the lower arm as the two rays. This angle will vary as per the position of our arm.

2) Angle formed between the two hands of the clock that are hinged at a point.

3) Angle formed between the two hands of a windmill. They are also hinged at a point, which is called the vertex of that angle.

#### Page No 176:

#### Question 2:

Three examples from our daily life are as follows:

1) Angle formed at the vertex of our elbow with the upper arm and the lower arm as the two rays. This angle will vary as per the position of our arm.

2) Angle formed between the two hands of the clock that are hinged at a point.

3) Angle formed between the two hands of a windmill. They are also hinged at a point, which is called the vertex of that angle.

#### Answer:

The vertex is B.

Arms of $\angle ABCarerays\overrightarrow{BA}and\overrightarrow{BC}$.

#### Page No 176:

#### Question 3:

The vertex is B.

Arms of $\angle ABCarerays\overrightarrow{BA}and\overrightarrow{BC}$.

#### Answer:

(i) Here, three angles are formed. They are $\angle ABC,\angle ACBand\angle BAC.$

(ii) Here, four angles are formed. They are $\angle ABC,\angle BCD,\angle CDAand\angle DAB$.

(iii) Here, eight angles are formed. They are $\angle ABC,\angle BCD,\angle CDA,\angle DAB,\angle ABD,\angle ADB,\angle CDB,\angle CBD$.

#### Page No 176:

#### Question 4:

(i) Here, three angles are formed. They are $\angle ABC,\angle ACBand\angle BAC.$

(ii) Here, four angles are formed. They are $\angle ABC,\angle BCD,\angle CDAand\angle DAB$.

(iii) Here, eight angles are formed. They are $\angle ABC,\angle BCD,\angle CDA,\angle DAB,\angle ABD,\angle ADB,\angle CDB,\angle CBD$.

#### Answer:

(i) Q and S are in the interior of $\angle $*AOB*.

(ii) P and R are in the exterior of $\angle $*AOB.*

(iii) A, O, B, N and T lie on the angle $\angle $AOB.

#### Page No 176:

#### Question 5:

(i) Q and S are in the interior of $\angle $*AOB*.

(ii) P and R are in the exterior of $\angle $*AOB.*

(iii) A, O, B, N and T lie on the angle $\angle $AOB.

#### Answer:

(i)False

Point *C* is on the angle $\angle $*AOC*.

(ii)True

Point *C lies *in the interior of $\angle $*AOD*.

(iii) False

Point *D* lies in the exterior of $\angle $*AOC*.

(iv) True

Point *B* lies in the exterior of $\angle $*AOD*.

(v) False

Point C lies in the interior of $\angle $AOB.

#### Page No 177:

#### Question 6:

(i)False

Point *C* is on the angle $\angle $*AOC*.

(ii)True

Point *C lies *in the interior of $\angle $*AOD*.

(iii) False

Point *D* lies in the exterior of $\angle $*AOC*.

(iv) True

Point *B* lies in the exterior of $\angle $*AOD*.

(v) False

Point C lies in the interior of $\angle $AOB.

#### Answer:

(i) $\angle $EPB

(ii) $\angle $PQC

(iii) $\angle $FQD

#### Page No 179:

#### Question 1:

(i) $\angle $EPB

(ii) $\angle $PQC

(iii) $\angle $FQD

#### Answer:

(i) $\angle $AOB is an obtuse angle since its measure is more than 90$\xb0$.

(ii) $\angle $COD is a right angle since its measure is 90$\xb0$.

(iii) $\angle $FOE is a straight angle since its measure is 180$\xb0$.

(iv) $\angle $POQ is a reflex angle since its measure is more than 180$\xb0$ but less than 360$\xb0$.

(v) $\angle $HOG is an acute angle since its measure is more than 0 but less than 90$\xb0$.

(vi) $\angle $POP is a complete angle since its measure is 360$\xb0$.

#### Page No 179:

#### Question 2:

(i) $\angle $AOB is an obtuse angle since its measure is more than 90$\xb0$.

(ii) $\angle $COD is a right angle since its measure is 90$\xb0$.

(iii) $\angle $FOE is a straight angle since its measure is 180$\xb0$.

(iv) $\angle $POQ is a reflex angle since its measure is more than 180$\xb0$ but less than 360$\xb0$.

(v) $\angle $HOG is an acute angle since its measure is more than 0 but less than 90$\xb0$.

(vi) $\angle $POP is a complete angle since its measure is 360$\xb0$.

#### Answer:

(i) Acute angle

This is because its measure is less than 90$\xb0$ but more than 0$\xb0$.

(ii) Obtuse angle

This is because its measure is more than 90$\xb0$ but less than 180$\xb0$

(iii) Obtuse angle

This is because its measure is more than 90$\xb0$ but less than 180$\xb0$.

(iv)Right angle

This is because its measure is 90$\xb0$.

(v) Reflex angle

This is because its measure is more than 180$\xb0$ but less than 360$\xb0$.

(vi) Complete angle

This is because its measure is 360$\xb0$.

(vii) Obtuse angle

This is because its measure is more than 90$\xb0$ but less than 180$\xb0$.

(viii) Obtuse angle

This is because its measure is more than 90$\xb0$ but less than 180$\xb0$.

(ix) Acute angle

This is because its measure is more than 0$\xb0$ but less than 90$\xb0$.

(x) Acute angle

This is because its measure is more than 0$\xb0$ but less than 90$\xb0$.

(xi) Zero angle

This is because its measure is zero.

(xii) Acute angle

This is because its measure is more than 0$\xb0$ but less than 90$\xb0$.

#### Page No 179:

#### Question 3:

(i) Acute angle

This is because its measure is less than 90$\xb0$ but more than 0$\xb0$.

(ii) Obtuse angle

This is because its measure is more than 90$\xb0$ but less than 180$\xb0$

(iii) Obtuse angle

This is because its measure is more than 90$\xb0$ but less than 180$\xb0$.

(iv)Right angle

This is because its measure is 90$\xb0$.

(v) Reflex angle

This is because its measure is more than 180$\xb0$ but less than 360$\xb0$.

(vi) Complete angle

This is because its measure is 360$\xb0$.

(vii) Obtuse angle

This is because its measure is more than 90$\xb0$ but less than 180$\xb0$.

(viii) Obtuse angle

This is because its measure is more than 90$\xb0$ but less than 180$\xb0$.

(ix) Acute angle

This is because its measure is more than 0$\xb0$ but less than 90$\xb0$.

(x) Acute angle

This is because its measure is more than 0$\xb0$ but less than 90$\xb0$.

(xi) Zero angle

This is because its measure is zero.

(xii) Acute angle

This is because its measure is more than 0$\xb0$ but less than 90$\xb0$.

#### Answer:

(i) One right angle has 90$\xb0$.

(ii) Two right angles have 90$\xb0$ + 90$\xb0$ = 180$\xb0$.

(iii) Three right angles have 90$\xb0$ + 90$\xb0$ + 90$\xb0$ = 270$\xb0$.

(iv) Four right angles have 90$\xb0$ + 90$\xb0$ + 90$\xb0$ + 90$\xb0$ = 360$\xb0$.

(v) $\frac{2}{3}\times 90=60\xb0$

(vi) $\left(1+\frac{1}{2}\right)rightangles=\frac{3}{2}\times 90\phantom{\rule{0ex}{0ex}}=135\xb0$

#### Page No 179:

#### Question 4:

(i) One right angle has 90$\xb0$.

(ii) Two right angles have 90$\xb0$ + 90$\xb0$ = 180$\xb0$.

(iii) Three right angles have 90$\xb0$ + 90$\xb0$ + 90$\xb0$ = 270$\xb0$.

(iv) Four right angles have 90$\xb0$ + 90$\xb0$ + 90$\xb0$ + 90$\xb0$ = 360$\xb0$.

(v) $\frac{2}{3}\times 90=60\xb0$

(vi) $\left(1+\frac{1}{2}\right)rightangles=\frac{3}{2}\times 90\phantom{\rule{0ex}{0ex}}=135\xb0$

#### Answer:

(i) At 3 o'clock the angle formed between the hour hand and the minute hand is right angle, i.e. 90$\xb0$.

(ii) At 6 o'clock the angle formed between the hour hand and the minute hand is a straight angle, i.e. 180$\xb0$.

(iii) At 12 o'clock the angle formed between the hour hand and the minute hand is a complete angle, i.e. 0$\xb0$.

This is because the hour hand and minute hand coincides to each other at 12 o'clock.

(iv) At 9 o'clock the angle formed between the hour hand and the minute hand is a right angle, i.e. 90$\xb0$.

#### Page No 179:

#### Question 5:

(i) At 3 o'clock the angle formed between the hour hand and the minute hand is right angle, i.e. 90$\xb0$.

(ii) At 6 o'clock the angle formed between the hour hand and the minute hand is a straight angle, i.e. 180$\xb0$.

(iii) At 12 o'clock the angle formed between the hour hand and the minute hand is a complete angle, i.e. 0$\xb0$.

This is because the hour hand and minute hand coincides to each other at 12 o'clock.

(iv) At 9 o'clock the angle formed between the hour hand and the minute hand is a right angle, i.e. 90$\xb0$.

#### Answer:

(i) Acute angle

(ii) Obtuse angle

(iii) Straight angle

#### Page No 182:

#### Question 1:

(i) Acute angle

(ii) Obtuse angle

(iii) Straight angle

#### Answer:

(i) $\angle AOB=45\xb0$

(ii) $\angle PQR=75\xb0$

(iii) $\angle DEF=135\xb0$

(iv) $\angle LMN=55\xb0$

(v) $\angle TSR=135\xb0$

(vi) $\angle GHI=75\xb0$

We have measured all the above angles by placing the protractor on one of the arms of the angle and measuring the angle through the other arm that coincides with the angle on the protractor.

#### Page No 182:

#### Question 2:

(i) $\angle AOB=45\xb0$

(ii) $\angle PQR=75\xb0$

(iii) $\angle DEF=135\xb0$

(iv) $\angle LMN=55\xb0$

(v) $\angle TSR=135\xb0$

(vi) $\angle GHI=75\xb0$

We have measured all the above angles by placing the protractor on one of the arms of the angle and measuring the angle through the other arm that coincides with the angle on the protractor.

#### Answer:

Steps to follow:

- Draw a ray QP with Q as the initial point.
- Place the protractor on QP. With its centre on Q, mark a point R against the given angle mark of the protractor.
- Join RQ. Now, PQR is the required angle.

(i)

(ii)

(iii)

(iv)

(v)

(vi)

(vii)

(viii)

#### Page No 182:

#### Question 3:

Steps to follow:

- Draw a ray QP with Q as the initial point.
- Place the protractor on QP. With its centre on Q, mark a point R against the given angle mark of the protractor.
- Join RQ. Now, PQR is the required angle.

(i)

(ii)

(iii)

(iv)

(v)

(vi)

(vii)

(viii)

#### Answer:

We can see that $\angle ABC=47\xb0$.

Steps to follow to construct angle $\angle $DEF equal to $\angle $ABC:

- Draw a ray EF with E as the initial point.
- Place the protractor on EF. With its centre at E, mark a point D against the angle 47$\xb0$ of the protractor.
- Join DE. $\angle $DEF = 47$\xb0$ = $\angle $ABC is the required angle.

#### Page No 182:

#### Question 4:

We can see that $\angle ABC=47\xb0$.

Steps to follow to construct angle $\angle $DEF equal to $\angle $ABC:

- Draw a ray EF with E as the initial point.
- Place the protractor on EF. With its centre at E, mark a point D against the angle 47$\xb0$ of the protractor.
- Join DE. $\angle $DEF = 47$\xb0$ = $\angle $ABC is the required angle.

#### Answer:

- Draw a line segment AB of length 6 cm.
- Mark point C on AB such that AC is equal to 4 cm.
- Place the protractor on AB such that the centre of the protractor is on C and its base lies along AB.
- Holding the protractor, mark a point D on the paper against the 90$\xb0$ mark of the protractor.
- Remove the protractor and draw a ray CD with C as the initial point.

#### Page No 182:

#### Question 1:

- Draw a line segment AB of length 6 cm.
- Mark point C on AB such that AC is equal to 4 cm.
- Place the protractor on AB such that the centre of the protractor is on C and its base lies along AB.
- Holding the protractor, mark a point D on the paper against the 90$\xb0$ mark of the protractor.
- Remove the protractor and draw a ray CD with C as the initial point.

#### Answer:

(c) On the angle

Vertex is the initial point of two rays between which the angle is formed. Therefore, it lies on the angle.

#### Page No 182:

#### Question 2:

(c) On the angle

Vertex is the initial point of two rays between which the angle is formed. Therefore, it lies on the angle.

#### Answer:

(c) an angle

The initial point is called the vertex.

#### Page No 182:

#### Question 3:

(c) an angle

The initial point is called the vertex.

#### Answer:

(c) straight angle

#### Page No 182:

#### Question 4:

(c) straight angle

#### Answer:

(b) right angle

#### Page No 182:

#### Question 5:

(b) right angle

#### Answer:

(b) an obtuse angle

This is because it is more than 90$\xb0$ but less than 180$\xb0$.

#### Page No 182:

#### Question 6:

(b) an obtuse angle

This is because it is more than 90$\xb0$ but less than 180$\xb0$.

#### Answer:

(d) a reflex angle

This is because it is more than 180$\xb0$ but less than 360$\xb0$.

#### Page No 182:

#### Question 7:

(d) a reflex angle

This is because it is more than 180$\xb0$ but less than 360$\xb0$.

#### Answer:

(c) 180$\xb0$

#### Page No 183:

#### Question 8:

(c) 180$\xb0$

#### Answer:

(c) a reflex angle

This is because it is more than 180$\xb0$ but less than 360$\xb0$.

#### Page No 183:

#### Question 9:

(c) a reflex angle

This is because it is more than 180$\xb0$ but less than 360$\xb0$.

#### Answer:

(d) a complete angle

This is because it completes the rotation of 360$\xb0$.

#### Page No 183:

#### Question 10:

(d) a complete angle

This is because it completes the rotation of 360$\xb0$.

#### Answer:

(b) more than 180$\xb0\mathrm{but}\mathrm{less}\mathrm{than}360\xb0$

#### Page No 183:

#### Question 11:

(b) more than 180$\xb0\mathrm{but}\mathrm{less}\mathrm{than}360\xb0$

#### Answer:

(b)

2 right angles = $2\times 90\xb0=180\xb0$ (straight angle)

#### Page No 183:

#### Question 12:

(b)

2 right angles = $2\times 90\xb0=180\xb0$ (straight angle)

#### Answer:

(b) 135$\xb0$

$\frac{3}{2}\mathrm{right}\mathrm{angle}=\frac{3}{2}\times 90\xb0\phantom{\rule{0ex}{0ex}}=135\xb0$

#### Page No 183:

#### Question 13:

(b) 135$\xb0$

$\frac{3}{2}\mathrm{right}\mathrm{angle}=\frac{3}{2}\times 90\xb0\phantom{\rule{0ex}{0ex}}=135\xb0$

#### Answer:

( c) 10$\xb0$

Number of spokes = 36

Measure of the angle of the wheel = Complete angle = 360$\xb0$

Angle between a pair of adjacent spokes=$\frac{\mathrm{Measure}\mathrm{of}\mathrm{angle}}{\mathrm{Number}\mathrm{of}\mathrm{spokes}}=\frac{360\xb0}{36}=10\xb0$

View NCERT Solutions for all chapters of Class 6