NCERT Solutions for Class 6 Maths Chapter 14 Practical Geometry (Ex 14.6) Exercise 14.6

NCERT Solutions for Class 6 Maths Chapter 14 Practical Geometry (Ex 14.6) Exercise 14.6

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Students can learn more advanced information about angle bisectors from NCERT Solutions Class 6 Maths Chapter 14 Exercise 14.6. Before beginning to solve the problems in the exercise, students must first review the examples covered to ensure they understand the concept. Additionally, students should regularly practise the problems if they want to achieve excellent exam results. Due to the fact that subject specialists created them, the questions are excellent for gaining the best insights into Geometry. After completing NCERT Solutions Class 6 Maths Chapter 14 Exercise 14.6, students may perform excellently with regard to questions related to Practical Geometry.

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Access Other Exercises of Class 6 Maths Chapter 14

Chapter 14 – Practical Geometry Exercises
Exercise 14.1
5 Questions & Solutions
Exercise 14.2
5 Questions & Solutions
Exercise 14.3
2 Questions & Solutions
Exercise 14.4
3 Questions & Solutions
Exercise 14.5
9 Questions & Solutions

NCERT Solutions for Class 6 Maths Chapter 14 Practical Geometry (Ex 14.6) Exercise 14.6

Exercise 14.6 to which the NCERT Solutions Class 6 Maths Chapter 14 Exercise 14.6 pertain is the last exercise in this chapter on Practical Geometry. There are nine questions in this exercise that require students to construct angles using a ruler and compass. The issues revolve around the subtopics of creating an angle of a given measure, creating a copy of an unknown measure, creating an angle bisector, and creating angles of special measures.

To determine the perpendicular bisector of the given angle, students must answer the first three questions. The fourth question asks students to divide an angle into four equal parts, while the fifth one asks them to use a ruler and compass to draw various angles. Students must create an angle and its bisector for questions six and seven. It is necessary to duplicate the given angles for the final two questions. Students will thoroughly understand the geometrical construction of various geometrical shapes after completing these sums. Students can advance their fundamental abilities in drawing angles in geometry by completing the NCERT solutions to class 6 Maths Chapter 14 Exercise 14.6. The NCERT Solutions Class 6 Maths Chapter 14 Exercise 14.6 are available in PDF format and includes several illustrations to help students visualize the steps needed to create constructions.

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Access NCERT Solution for Class 6 Maths Chapter 14 – Practical Geometry

The answers to the questions included in this exercise are covered in NCERT Solutions Class 6 Maths Chapter 14 Exercise 14.6. The NCERT Solutions Class 6 Maths Chapter 14 Exercise 14.6 cover angles and their construction, the bisector of an angle, angles of special measures, and illustrative examples. Exercises are provided for students to improve students understanding of the concepts by working through NCERT Solutions Class 6 Maths Chapter 14 Exercise 14.6. These concepts are crucial for the exam. Students can prepare for the exams by downloading the NCERT Solutions Class 6 Maths Chapter 14 Exercise 14.6. However, students should access the NCERT Solutions Class 6 Maths Chapter 14 Exercise 14.6 from the Extramarks website and mobile application.

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Exercise 14.6

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NCERT Solutions for Class 6 Maths Chapter 14 Practical Geometry Exercise 14.6

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Q.1

Draw ∠POQ of measure 75°and find its line of symmetry.

Ans.Steps of construction:
1. Draw a ray OP.

2. Mark an arc of any radius with centre O. This arc intersects OP at the point A.
3. Mark another arc of the same radius with centre A, it intersects earlier arc at the point B.
4. Arc of same radius with centre B intersects the earliest arc at R.
5. The arcs drawn of any radius with centre B and R respectively intersect at the point S.
6. Draw ray OC through the point S.
6. Mark another arc of any radius with centre U (intersection point of arc and OC) and B which intersect at T.
7. Draw ray OQ through the point T
8. Draw two arcs of any radius with centre W (intersection point of arc and OQ) and A. These arcs intersect at the point V. Therefore, line OV is the line of symmetry for angle POQ.

Q.2 Draw an angle of measure 147° and construct its bisector.

Ans.Steps of construction:
1. Draw a ray OP.

2. Draw an angle of 147° with the help of protractor at point O.

3. Draw an arc of any radius with centre O which intersects OP at A and OQ at B.
4. Mark two arcs of any radius with centre A and B, which intersect each other at C.
5. Draw ray OR through C. Therefore, OR is bisector of angle POQ.

Q.3 Draw a right angle and construct its bisector.

Ans.Steps of construction:

1. Draw a ray OP.
2. Mark an arc of any radius with centre O, which intersects ray OP at the point A.
3. Mark another arc of same radius with centre A which intersects earlier arc at B.
4. Mark an arc of same radius with centre B which intersects the earliest arc at the point C.
5. Mark two arcs of any radius with centre B and C respectively which intersect at the point R.
6. Draw ray OQ through the point R. In this way we get right angle POQ.
7. Again mark two arcs of any radius with centre A and D (intersection point of arc and OQ), which intersect each other at E.
8. Draw ray OS through E. Therefore, OS is bisector of angle POQ.

Q.4 Draw an angle of measure 153° and divide it into four equal parts.

Ans.

Steps of construction:
1. Draw a ray OP.

2. Draw an angle of 153° with the help of protractor at point O.

3. Taking O as centre draw an arc of any radius which cuts OP at A and OQ at B.
4. Mark two arcs of any radius with centre A and B which intersect each other at C.
5. Draw ray OR through C. Ray OR is bisector of angle POQ.

6. Mark two arcs of any radius with centre A and D which intersect at E.
7. Draw ray OS through the point E. OS is bisector of angle POR.
6. Draw two arcs of any radius with centre D and B, which intersect at F.
8. Draw ray OT through the point F. Therefore, by observation we see rays OS, OR and OT divide the angle POQ into four equal parts.

Q.5 Construct with ruler and compasses, angles of following measures:
(a) 60° (b) 30° (c) 90°
(d) 120° (e) 45° (f) 135°

Ans.

(a) Steps of construction:
1. Draw a ray OP.
2. Mark an arc of any radius with centre O. This arc intersects OP at the point A.
3. Mark another arc of the same radius with centre A, it intersects earlier arc at the point B.
4. Draw ray OQ through the point B.Therefore, angle POQ is required angle of 60°.

(b) Steps of construction:
1. Draw a ray OP.
2. Mark an arc of any radius with centre O. This arc intersects OP at the point A.
3. Mark another arc of the same radius with centre A, it intersects earlier arc at the point B.
4. Draw a ray OQ through the point B.
5. Mark two arcs of any radius with centre A and B, which intersect at point C.
6. Draw ray OR through point C. Therefore, angle POR is required angle of 30°.

(c) Steps of construction:
1. Draw a ray OP.
2. Mark an arc of any radius with centre O, which intersects ray OP at the point A.
3. Mark another arc of same radius with centre A which intersects earlier arc at B.
4. Mark an arc of same radius with centre B which intersects the earliest arc at the point C.
5. Mark two arcs of any radius with centre B and C respectively which intersect at the point R.
6. Draw ray OQ through the point R. In this way we get right angle POQ.

(d) Steps of construction:
1. Draw a ray OP.
2. Mark an arc of any radius with centre O. This arc intersects OP at the point A.
3. Mark another arc of the same radius with centre A, it intersects earlier arc at the point B.
4. Draw an arc with centre B of same radius. This arc intersects the earliest arc at the point C.
5. Draw ray OQ through the point C. Therefore, angle POQ is required angle of 120°.

(e) Steps of construction:
1. Draw a ray OP.
2. Mark an arc of any radius with centre O, which intersects ray OP at the point A.
3. Mark another arc of same radius with centre A which intersects earlier arc at B.
4. Mark an arc of same radius with centre B which intersects the earliest arc at the point C.
5. Mark two arcs of any radius with centre B and C respectively which intersect at the point R.
6. Draw ray OQ through the point R. In this way we get right angle POQ.
7. Mark two arcs of any radius with centre A and D, which intersect at E.
8. Draw a ray OS through the point E. Therefore, POS is required angle of 45°.

(f) Steps of construction:
1. Draw a line PR.
2. Take a point O on the line.
3. Draw a semi-circle of any radius with centre O.
4. Mark two arcs of any radius with centre A and B respectively which intersect at R.
5. Draw a ray OQ through the point D.
6. Mark two arcs with centre D and B which intersect at E.
7. Draw ray OS through the point E. Therefore, angle POS is required angle of 135°.

Q.6 Draw an angle of measure 45° and bisect it.

Ans.

Steps of construction:
1. Draw a ray OP.
2. Mark an arc of any radius with centre O, which intersects ray OP at the point A.
3. Mark another arc of same radius with centre A which intersects earlier arc at B.
4. Mark an arc of same radius with centre B which intersects the earliest arc at the point C.
5. Mark two arcs of any radius with centre B and C respectively which intersect at the point R.
6. Draw ray OQ through the point R. In this way we get right angle POQ.
7. Mark two arcs of any radius with centre A and D (intersection point of arc and OQ), which intersect at E.
8. Draw a ray OS through the point E.
9. Mark two arcs of any radius with centre A and G (intersection point of arc and OS), which intersect at F.
10. Draw ray OT through the point F. Therefore, angle POS is required angle of measure 45° and OT is bisector of angle POS.

Q.7 Draw an angle of measure 135° and bisect it.

Ans.

Steps of construction:
1. Draw a line MN.
2. Take a point O on the line.
3. Draw an arc of any radius with centre O which cuts the line MN at A and B.
4. Mark two arcs of radius more than half of AB with centre A and B respectively which intersect at R.
5. Draw a ray OQ through the point R. Let the ray OQ intersects the arc in (3) at D.
6. Mark two arcs with centre D and B of radius more than half of DB which intersect at E.
7. Draw ray OS through the point E. Therefore, angle NOS is required angle of 135°.
8. Mark two arcs of radius more than half of AC with centre A and C respectively which intersect at F.
9. Draw ray OT through the intersection point F. Therefore, angle NOT is the bisector of angle NOS.

Q.8 Draw an angle of 70°. Make a copy of it using only a straight edge and compasses.

Ans.

Steps of construction:
1. Draw a ray OA.
2. Draw an angle of 70° at point O with the help of protractor.


3. Mark an arc with centre O which cuts OA and OB at C and D respectively.
4. Draw a ray QP and mark an arc with the same radius and centre Q on ray QP.
5. Set your compasses to the length CD with the same radius and mark an arc with centre T which cuts earlier arc at the point R.
6. Draw ray QS through the point R. Therefore, angle PQS is required angle of 70°.

Q.9 Draw an angle of 40°. Copy its supplementary angle.

Ans.

Steps of construction:
Draw a line PA and mark a point O on it.
Draw an angle of 40° at point O with the help of protractor.

 

 

 

 

 

3. Angle POB is supplementary of 40°.
4. Taking O as centre, draw an arc between the rays of angle POB which cuts PO and OB at D and C respectively.

 

 

 

5. Now draw a line m and take a point S on it. Taking same radius and S as centre draw an arc. This arc cuts line m at point T.
6. Set your compasses to the length CD with the same radius and mark an arc with centre T which cuts earlier arc at the point R.
7. Join S and R. SR is the required ray which makes a supplementary angle of 40° with line m or makes an angle of 140°.

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