*According to the latest update on the CBSE Syllabus 2023-24, this chapter has been removed.
NCERT Solutions or Class 6 Maths Chapter 14 Practical Geometry Exercise 14.6 covers the answers to the questions present in this exercise. Angles and their construction, the bisector of an angle and angles of special measures, along with illustrative examples, are covered under Exercise 14.6 of Chapter 14. Students are provided with exercise-wise NCERT Solutions to get better acquainted with the concepts, which are important from the exam point of view.
NCERT Solutions for Class 6 Maths Chapter 14 Practical Geometry Exercise 14.6
Access NCERT Solutions for Class 6 Chapter 14: Practical Geometry Exercise 14.6
1. Draw ∠POQ of measure 75° and find its line of symmetry.
Solutions:
The following steps are used to construct an angle of 750 and its line of symmetry:
(i) Draw a line l and mark two points, O and Q, on it. Draw an arc of convenient radius while taking centre as O. Let this intersect line l at R.
(ii) Taking R as the centre and with the same radius as before, draw an arc such that it intersects the previously drawn arc at S.
(iii) By taking the same radius as before and S as the centre, draw an arc intersecting the arc at point T, as shown in the figure.
(iv) Take S and T as the centre, and draw an arc of the same radius such that they intersect each other at U.
(v) Join OU. Let it intersect the arc at V. Now, take S and V as centres draw arcs with a radius of more than 1/2 SV. Let these intersect each other at P, then Join OP. Now, OP is the ray making 750 with the line l.
(vi) Let this ray intersect the major arc at point W. By taking R and W as centres, draw arcs with a radius of more than 1/2 RW in the interior angle of 750. Let these intersect each other at point X. Join OX.
OX is the line of symmetry for the ∠POQ = 750.
2. Draw an angle of measure 147° and construct its bisector.
Solutions:
The following steps are used to construct an angle of measure 1470 and its bisector:
(i) Draw a line l and mark point O on it. Place the centre of the protractor at point O and the zero edge along line l.
(ii) Mark point A at an angle of measure 1470 and join OA. Now, OA is the required ray making 1470 with line l.
(iii) By taking point O as the centre, draw an arc of the convenient radius. Let this intersect both rays of angle 1470 at points A and B.
(iv) By taking A and B as centres, draw arcs of radius more than 1/2 AB in the interior angle of 1470. Let these intersect each other at point C. Join OC.
OC is the required bisector of 1470 angle.
3. Draw a right angle and construct its bisector.
Solutions:
The following steps are used to construct a right angle and its bisector:
(i) Draw a line l and mark a point P on it. Draw an arc of the convenient radius by taking point P as the centre. Let this intersect line l at R.
(ii) Draw an arc by taking R as the centre and with the same radius as before such that it intersects the previously drawn arc at S.
(iii) Take S as the centre and with the same radius as before, draw an arc intersecting the arc at T, as shown in the figure.
(iv) By taking S and T as centres, draw arcs of the same radius such that they intersect each other at U.
(v) Join PU. PU is the required ray making a right angle with the line l. Let this intersect the major arc at point V.
(vi) Now, take R and V as centres, and draw arcs with a radius of more than 1/2 RV to intersect each other at point W. Join PW.
PW is the required bisector of this right angle.
4. Draw an angle of measure 153° and divide it into four equal parts.
Solutions:
The following steps are used to construct an angle of measure 1530 and its bisector:
(i) Draw a line l and mark a point O on it. Place the centre of the protractor at point O and the zero edge along line l.
(ii) Mark a point A at the measure of angle 1530, and join OA. Now, OA is the required ray making 1530 with line l.
(iii) Draw an arc of the convenient radius by taking point O as the centre. Let this intersect both rays of angle 1530 at points A and B.
(iv) Take A and B as centres and draw arcs of radius more than 1/2 AB in the interior of an angle of 1530. Let these intersect each other at C. Join OC.
(v) Let OC intersect the major arc at point D. Draw arcs of radius more than 1/2 AD with A and D as centres and also D and B as centres. Let these are intersecting each other at points E and F, respectively. Now join OE and OF.
OF, OC and OE are the rays dividing the 1530 angle into four equal parts.
5. Construct with ruler and compasses angles of the following measures:
(a) 60°
(b) 30°
(c) 90°
(d) 120°
(e) 45°
(f) 135°
Solutions:
(a) 600
The following steps are followed to construct an angle of 600:
(i) Draw a line l and mark a point P on it. Take P as the centre, and with a convenient radius, draw an arc of a circle such that it intersects the line l at Q.
(ii) Take Q as the centre and with the same radius as before, draw an arc intersecting the previously drawn arc at point R.
(iii) Join PR. PR is the required ray making 600 with the line l.
(b) 300
The following steps are followed to construct an angle of 300:
(i) Draw a line l and mark a point P on it. By taking P as the centre and with a convenient radius, draw an arc of a circle such that it intersects the line l at Q.
(ii) Take Q as the centre and with the same radius as before, draw an arc intersecting the previously drawn arc at point R.
(iii) By taking Q and R as centres and with a radius of more than 1/2 RQ draw arcs such that they intersect each other at S. Join PS, which is the required ray making 300 with the line l.
(c) 900
The following steps are used to construct an angle of measure 900:
(i) Draw a line l and mark a point P on it. Take P as the centre, and with a convenient radius, draw an arc of a circle such that it intersects the line l at Q.
(ii) Take Q as the centre, and with the same radius as before, draw an arc intersecting the previously drawn arc at R.
(iii) By taking R as the centre and with the same radius as before, draw an arc intersecting the arc at S, as shown in the figure.
(iv) Now, take R and S as the centre, and draw an arc of the same radius to intersect each other at T.
(v) Join PT, which is the required ray, making 900 with line l.
(d) 1200
The following steps are used to construct an angle of measure 1200:
(i) Draw a line l and mark a point P on it. Taking P as the centre and with a convenient radius, draw an arc of the circle such that it intersects the line l at Q.
(ii) By taking Q as the centre and with the same radius as before, draw an arc intersecting the previously drawn arc at R.
(iii) Take R as the centre and with the same radius as before, draw an arc such that it intersects the arc at S, as shown in the figure.
(iv) Join PS, which is the required ray making 1200 with the line l.
(e) 450
The following steps are used to construct an angle of measure 450:
(i) Draw a line l and mark a point P on it. Take P as the centre, and with a convenient radius, draw an arc of a circle such that it intersects the line l at Q.
(ii) Take Q as the centre, and with the same radius as before, draw an arc intersecting the previously drawn arc at R.
(iii) By taking R as the centre and with the same radius as before, draw an arc such that it intersects the arc at S, as shown in the figure.
(iv) Take R and S as centres and draw arcs of the same radius such that they intersect each other at T.
(v) Join PT. Let this intersect the major arc at point U.
(vi) Now, take Q and U as centres and draw arcs with a radius of more than 1/2 QU to intersect each other at point V. Join PV.
PV is the required ray making 450 with the line l.
(f) 1350
The following steps are used to construct an angle of measure 1350:
(i) Draw a line l and mark a point P on it. Taking P as the centre and with a convenient radius, draw a semicircle which intersects the line l at Q and R, respectively.
(ii) By taking R as the centre and with the same radius as before, draw an arc intersecting the previously drawn arc at S.
(iii) Taking S as the centre and with the same radius as before, draw an arc such that it intersects the arc at T, as shown in the figure.
(iv) Take S and T as centres, and draw arcs of the same radius to intersect each other at U.
(v) Join PU. Let this intersect the arc at V. Now, take Q and V as centres and with a radius of more than 1/2 QV, draw arcs to intersect each other at W.
(vi) Join PW, which is the required ray making 1350 with the line l.
6. Draw an angle of measure 45° and bisect it.
Solutions:
The following steps are used to construct an angle of measure 450 and its bisector:
(i) Using the protractor, a ∠POQ of 450 measure may be formed on a line l.
(ii) Draw an arc of the convenient radius with the centre as O. Let this intersect both rays of angle 450 at points A and B.
(iii) Take A and B as centres and draw arcs of radius more than 1/2 AB in the interior of an angle of 450. Let these intersect each other at C. Join OC.
OC is the required bisector of 450 angle.
7. Draw an angle of measure 135° and bisect it.
Solutions:
The following steps are used to construct an angle of measure 1350 and its bisector:
(i) By using a protractor, a ∠POQ of 1350 measure may be formed on a line l.
(ii) Draw an arc of the convenient radius by taking O as the centre. Let this intersect both rays of angle 1350 at points A and B, respectively.
(iii) Take A and B as centres and draw arcs of a radius of more than 1/2 AB in the interior of an angle of 1350. Let these intersect each other at C. Join OC.
OC is the required bisector of 1350 angle.
8. Draw an angle of 700. Make a copy of it using only a straight edge and compasses.
Solutions:
The following steps are used to construct an angle of measure 700 and its copy:
(i) Draw a line l and mark a point O on it. Now, place the centre of the protractor at point O and the zero edge along line l.
(ii) Mark a point A at an angle of measure 700. Join OA. Now, OA is the ray making 700 with line l. With point O as the centre, draw an arc of a convenient radius in the interior of 700 angle. Let this intersect both rays of angle 700 at points B and C, respectively.
(iii) Draw a line m and mark a point P on it. Again, draw an arc with the same radius as before and P as the centre. Let it cut the line m at point D.
(iv) Adjust the compasses up to the length of BC. With this radius, draw an arc taking D as the centre, which intersects the previously drawn arc at point E.
(v) Join PE. Here, PE is the required ray which makes the same angle of measure 700 with the line m.
9. Draw an angle of 400. Copy its supplementary angle.
Solutions:
The following steps are used to construct an angle of measure 450 and a copy of its supplementary angle:
(i) Draw a line segment
and mark a point O on it. Place the centre of the protractor at point O and the zero edge along the line segment.
.
(ii) Mark a point A at an angle of measure 400. Join OA. Here. OA is the required ray, making 400 with
. ∠POA is the supplementary angle of 400.
(iii) With point O as the centre, draw an arc of convenient radius in the interior of ∠POA. Let this intersect both rays of ∠POA at points B and C, respectively.
(iv) Draw a line m and mark a point S on it. Again draw an arc by taking S as the centre with the same radius as used before. Let it cut the line m at point T.
(v) Now, adjust the compasses up to the length of BC. Taking T as the centre, draw an arc with this radius which will intersect the previously drawn arc at point R.
(vi) Join RS. Here, RS is the required ray which makes the same angle with the line m as the supplementary of 400 [i.e., 1400].
Also, explore –
NCERT Solutions for Class 6 Maths Chapter 14
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