RD Sharma Solutions: Angles (Exercise 11.1)

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Exercise 11.1                                                                             page: 11.5
1. Give three examples of angles from your environment.
Solution:

The three examples of angles are
The angle formed by the two adjacent fingers of our hand
The angle formed by two adjacent walls of a room
The angle formed by the hour hand and minute hand of a clock.

2. Write the arms and the vertex of ? LMP given in Fig. 11.14.

Solution:

The vertex of ? LMP is M and the arms are ML and MP.

3. How many angles are formed in the figures 11.15 (i), (ii) and (iii)? Name them.

Solution:

(i) Three angles are formed in figure (i) namely ? ABC, ? ACB and ? BAC.

(ii) Four angles are formed in figure (ii) namely ? ABC, ? BCD, ? CDA and ? DAB.

(iii) Eight angles are formed in figure (iii) namely ? ABC, ? BCD, ? CDA, ? DAB, ? CAB, ? CAD, ? BCA and
? ACD.

4. In Fig. 11.16, list the points which are: (i) in the interior of ? P (ii) in the exterior of ? P and (iii) lie on ?
P.
Page 2

Exercise 11.1                                                                             page: 11.5
1. Give three examples of angles from your environment.
Solution:

The three examples of angles are
The angle formed by the two adjacent fingers of our hand
The angle formed by two adjacent walls of a room
The angle formed by the hour hand and minute hand of a clock.

2. Write the arms and the vertex of ? LMP given in Fig. 11.14.

Solution:

The vertex of ? LMP is M and the arms are ML and MP.

3. How many angles are formed in the figures 11.15 (i), (ii) and (iii)? Name them.

Solution:

(i) Three angles are formed in figure (i) namely ? ABC, ? ACB and ? BAC.

(ii) Four angles are formed in figure (ii) namely ? ABC, ? BCD, ? CDA and ? DAB.

(iii) Eight angles are formed in figure (iii) namely ? ABC, ? BCD, ? CDA, ? DAB, ? CAB, ? CAD, ? BCA and
? ACD.

4. In Fig. 11.16, list the points which are: (i) in the interior of ? P (ii) in the exterior of ? P and (iii) lie on ?
P.

Solution:

(i) The points which are in the interior of ? P are J and C.

(ii) The points which are in the exterior of ? P are B and D.

(iii) The points which lie on ? P are A, P and M.

5. In Fig. 11.17, write another name for:

(i) ? 1
(ii) ? 2
(iii) ? 3
(iv) ? 4
Solution:

(i) From the figure, another name for ? 1 is ? BOD or ? DOB.

(ii) From the figure, another name for ? 2 is ? BOC or ? COB.

(iii) From the figure, another name for ? 3 is ? COA or ? AOC.

(iv) From the figure, another name for ? 4 is ? AOD or ? DOA.

6. In Fig. 11.18, write another name for:
Page 3

Exercise 11.1                                                                             page: 11.5
1. Give three examples of angles from your environment.
Solution:

The three examples of angles are
The angle formed by the two adjacent fingers of our hand
The angle formed by two adjacent walls of a room
The angle formed by the hour hand and minute hand of a clock.

2. Write the arms and the vertex of ? LMP given in Fig. 11.14.

Solution:

The vertex of ? LMP is M and the arms are ML and MP.

3. How many angles are formed in the figures 11.15 (i), (ii) and (iii)? Name them.

Solution:

(i) Three angles are formed in figure (i) namely ? ABC, ? ACB and ? BAC.

(ii) Four angles are formed in figure (ii) namely ? ABC, ? BCD, ? CDA and ? DAB.

(iii) Eight angles are formed in figure (iii) namely ? ABC, ? BCD, ? CDA, ? DAB, ? CAB, ? CAD, ? BCA and
? ACD.

4. In Fig. 11.16, list the points which are: (i) in the interior of ? P (ii) in the exterior of ? P and (iii) lie on ?
P.

Solution:

(i) The points which are in the interior of ? P are J and C.

(ii) The points which are in the exterior of ? P are B and D.

(iii) The points which lie on ? P are A, P and M.

5. In Fig. 11.17, write another name for:

(i) ? 1
(ii) ? 2
(iii) ? 3
(iv) ? 4
Solution:

(i) From the figure, another name for ? 1 is ? BOD or ? DOB.

(ii) From the figure, another name for ? 2 is ? BOC or ? COB.

(iii) From the figure, another name for ? 3 is ? COA or ? AOC.

(iv) From the figure, another name for ? 4 is ? AOD or ? DOA.

6. In Fig. 11.18, write another name for:

(i) ? 1
(ii) ? 2
(iii) ? 3
Solution:

(i) From the figure, another name for ? 1 is ? EPB or ? BPE.

(ii) From the figure, another name for ? 2 is ? CQP or ? PQC.

(iii) From the figure, another name for ? 3 is ? DQF or ? FQD.

7. In Fig. 11.19, which of the following statements are true:

(i) Point B is the interior of ? AOB.
(ii) Point B is the interior of ? AOC.
(iii) Point A is the interior of ? AOD.
(iv) Point C is the exterior of ? AOB.
(v) Point D is the exterior of ? AOC.
Solution:

(i) False. B lies on ? AOB.

(ii) True

(iii) False. A lies on ? AOD.

(iv) True

(v) True

8. Which of the following statements are true:
(i) The vertex of an angle lies in its interior.
(ii) The vertex of an angle lies in its exterior.
Page 4

Exercise 11.1                                                                             page: 11.5
1. Give three examples of angles from your environment.
Solution:

The three examples of angles are
The angle formed by the two adjacent fingers of our hand
The angle formed by two adjacent walls of a room
The angle formed by the hour hand and minute hand of a clock.

2. Write the arms and the vertex of ? LMP given in Fig. 11.14.

Solution:

The vertex of ? LMP is M and the arms are ML and MP.

3. How many angles are formed in the figures 11.15 (i), (ii) and (iii)? Name them.

Solution:

(i) Three angles are formed in figure (i) namely ? ABC, ? ACB and ? BAC.

(ii) Four angles are formed in figure (ii) namely ? ABC, ? BCD, ? CDA and ? DAB.

(iii) Eight angles are formed in figure (iii) namely ? ABC, ? BCD, ? CDA, ? DAB, ? CAB, ? CAD, ? BCA and
? ACD.

4. In Fig. 11.16, list the points which are: (i) in the interior of ? P (ii) in the exterior of ? P and (iii) lie on ?
P.

Solution:

(i) The points which are in the interior of ? P are J and C.

(ii) The points which are in the exterior of ? P are B and D.

(iii) The points which lie on ? P are A, P and M.

5. In Fig. 11.17, write another name for:

(i) ? 1
(ii) ? 2
(iii) ? 3
(iv) ? 4
Solution:

(i) From the figure, another name for ? 1 is ? BOD or ? DOB.

(ii) From the figure, another name for ? 2 is ? BOC or ? COB.

(iii) From the figure, another name for ? 3 is ? COA or ? AOC.

(iv) From the figure, another name for ? 4 is ? AOD or ? DOA.

6. In Fig. 11.18, write another name for:

(i) ? 1
(ii) ? 2
(iii) ? 3
Solution:

(i) From the figure, another name for ? 1 is ? EPB or ? BPE.

(ii) From the figure, another name for ? 2 is ? CQP or ? PQC.

(iii) From the figure, another name for ? 3 is ? DQF or ? FQD.

7. In Fig. 11.19, which of the following statements are true:

(i) Point B is the interior of ? AOB.
(ii) Point B is the interior of ? AOC.
(iii) Point A is the interior of ? AOD.
(iv) Point C is the exterior of ? AOB.
(v) Point D is the exterior of ? AOC.
Solution:

(i) False. B lies on ? AOB.

(ii) True

(iii) False. A lies on ? AOD.

(iv) True

(v) True

8. Which of the following statements are true:
(i) The vertex of an angle lies in its interior.
(ii) The vertex of an angle lies in its exterior.

(iii) The vertex of an angle lies on it.
Solution:

(i) False.

(ii) False.

(iii) True.

9. By simply looking at the pair of angles given in Fig. 11.20, state which of the angles in each of the pairs is
greater:

Solution:

(i) From the figure we know that ? AOB > ? DEF.

(ii) From the figure we know that ? PQR > ? LMN.

(iii) From the figure we know that ? UVW > ? XYZ.

10. By using tracing paper compare the angles in each of the pairs given in Fig. 11.21.
Page 5

Exercise 11.1                                                                             page: 11.5
1. Give three examples of angles from your environment.
Solution:

The three examples of angles are
The angle formed by the two adjacent fingers of our hand
The angle formed by two adjacent walls of a room
The angle formed by the hour hand and minute hand of a clock.

2. Write the arms and the vertex of ? LMP given in Fig. 11.14.

Solution:

The vertex of ? LMP is M and the arms are ML and MP.

3. How many angles are formed in the figures 11.15 (i), (ii) and (iii)? Name them.

Solution:

(i) Three angles are formed in figure (i) namely ? ABC, ? ACB and ? BAC.

(ii) Four angles are formed in figure (ii) namely ? ABC, ? BCD, ? CDA and ? DAB.

(iii) Eight angles are formed in figure (iii) namely ? ABC, ? BCD, ? CDA, ? DAB, ? CAB, ? CAD, ? BCA and
? ACD.

4. In Fig. 11.16, list the points which are: (i) in the interior of ? P (ii) in the exterior of ? P and (iii) lie on ?
P.

Solution:

(i) The points which are in the interior of ? P are J and C.

(ii) The points which are in the exterior of ? P are B and D.

(iii) The points which lie on ? P are A, P and M.

5. In Fig. 11.17, write another name for:

(i) ? 1
(ii) ? 2
(iii) ? 3
(iv) ? 4
Solution:

(i) From the figure, another name for ? 1 is ? BOD or ? DOB.

(ii) From the figure, another name for ? 2 is ? BOC or ? COB.

(iii) From the figure, another name for ? 3 is ? COA or ? AOC.

(iv) From the figure, another name for ? 4 is ? AOD or ? DOA.

6. In Fig. 11.18, write another name for:

(i) ? 1
(ii) ? 2
(iii) ? 3
Solution:

(i) From the figure, another name for ? 1 is ? EPB or ? BPE.

(ii) From the figure, another name for ? 2 is ? CQP or ? PQC.

(iii) From the figure, another name for ? 3 is ? DQF or ? FQD.

7. In Fig. 11.19, which of the following statements are true:

(i) Point B is the interior of ? AOB.
(ii) Point B is the interior of ? AOC.
(iii) Point A is the interior of ? AOD.
(iv) Point C is the exterior of ? AOB.
(v) Point D is the exterior of ? AOC.
Solution:

(i) False. B lies on ? AOB.

(ii) True

(iii) False. A lies on ? AOD.

(iv) True

(v) True

8. Which of the following statements are true:
(i) The vertex of an angle lies in its interior.
(ii) The vertex of an angle lies in its exterior.

(iii) The vertex of an angle lies on it.
Solution:

(i) False.

(ii) False.

(iii) True.

9. By simply looking at the pair of angles given in Fig. 11.20, state which of the angles in each of the pairs is
greater:

Solution:

(i) From the figure we know that ? AOB > ? DEF.

(ii) From the figure we know that ? PQR > ? LMN.

(iii) From the figure we know that ? UVW > ? XYZ.

10. By using tracing paper compare the angles in each of the pairs given in Fig. 11.21.

Solution:

(i) From the figure we know that ? PQR > ? AOB.

(ii) From the figure we know that ? UVW > ? LMN.

(iii) From the figure we know that ? RST > ? XYZ.

(iv) From the figure we know that ? PQR > ? EFG.

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Mathematics (Maths) Class 6

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FAQs on Angles (Exercise 11.1) RD Sharma Solutions - Mathematics (Maths) Class 6

 1. What are angles in mathematics?
Ans. In mathematics, angles are geometric figures formed by two rays or line segments that share a common endpoint called the vertex. Angles are measured in degrees and are used to describe the amount of rotation or separation between two lines or line segments.
 2. How do you measure angles?
Ans. Angles can be measured using a protractor. To measure an angle, place the center of the protractor on the vertex of the angle and align one of the rays with the zero degree mark. Then, read the measurement where the other ray intersects the protractor scale.
 3. What are the different types of angles?
Ans. There are several types of angles, including: - Acute angle: An angle that measures less than 90 degrees. - Right angle: An angle that measures exactly 90 degrees. - Obtuse angle: An angle that measures more than 90 degrees but less than 180 degrees. - Straight angle: An angle that measures exactly 180 degrees. - Reflex angle: An angle that measures more than 180 degrees but less than 360 degrees.
 4. How do you classify angles based on their measurements?
Ans. Angles can be classified into different categories based on their measurements: - Acute angles: Measuring less than 90 degrees. - Right angles: Measuring exactly 90 degrees. - Obtuse angles: Measuring more than 90 degrees but less than 180 degrees. - Straight angles: Measuring exactly 180 degrees. - Reflex angles: Measuring more than 180 degrees but less than 360 degrees.
 5. How can angles be used in real-life situations?
Ans. Angles are used in various real-life situations, such as: - Architecture and construction: Angles are used to determine the slope and inclination of roofs, stairs, and other structural elements. - Navigation: Angles are used in navigation systems to calculate directions and distances. - Sports: Angles are used in sports like billiards, golf, and bowling to calculate trajectories and aim shots. - Engineering: Angles are used in engineering designs to determine the angles of intersection or inclination in various components. - Astronomy: Angles are used in astronomy to measure the positions and movements of celestial objects.

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