NCERT Solutions for Class 6 Maths Chapter 14 Practical Geometry Ex 14.6
NCERT Solutions for Class 6 Maths Chapter 14 Practical Geometry Ex 14.6
These NCERT Solutions for Class 6 Maths Chapter 14 Practical Geometry Ex 14.6 Questions and Answers are prepared by our highly skilled subject experts.
NCERT Solutions for Class 6 Maths Chapter 14 Practical Geometry Exercise 14.6
Question 1.
Draw ∠POQ of measure 75° and find its line of symmetry.
Answer:
Steps of construction:
(a) Draw a line l and mark a point O on it.
(b) Place the pointer of the compasses at O and draw an arc of any radius which intersects the line l at A.
(c) Taking same radius, with centre A, cut the previous arc at B.
(d) Join OB, then ∠BOA = 60 .
(e) Taking same radius, with centre B, cut the previous arc at C.
(f) Draw bisector of ∠BOC. The angle is of 90 . Mark it at D. Thus, ∠DOA = 90°
Question 2.
Draw an angle of measure 147° and construct its bisector.
Answer:
Steps of construction:
(d) Taking P as centre and radius more than half of PQ, draw an arc.
(e) Taking Q as centre and with the same radius, draw another arc which intersects the previous at R.
(f) Join OR and produce it.
Question 3.
Draw a right angle and construct its bisector.
Answer:
Steps of construction:
(a) Draw a line PQ and take a point O on it.
(b) Taking O as centre and convenient radius, draw an arc which intersects PQ at A and B.
(c) Taking A and B as centres and radius more than half of AB, draw two arcs which intersect each other at C.
(d) Join OC. Thus, ∠COQ is the required right angle.
(e) Taking B and E as centre and radius more than half of BE, draw two arcs which intersect each other at the point D.
Question 4.
Draw an angle of measure 153° and divide it into four equal parts.
Answer:
Steps of construction:
Question 5.
Construct with ruler and compasses, angles of following measures:
(a) 60°
(b) 30°
(c) 90°
(d) 120°
(e) 45°
(f) 135°
Answer:
Steps of construction:
(a) 60°
(iii) Taking P as centre and same radius, cut previous arc at Q.
(iv) Join OQ.
Thus, ∠BOA is required angle of 60°.
(b) 30°
(iii) Taking P as centre and same radius, cut previous arc at Q.
(iv) Join OQ. Thus, ∠BOA is required angle of 60°.
(v) Put the pointer on P and mark an arc.
(vi) Put the pointer on Q and with same radius, cut the previous arc at C. Thus, ∠COA is required angle of 30°.
(c) 90°
- Taking X as centre and same radius, cut previous arc at Y.
- Taking Y as centre and same radius, draw another arc intersecting the same arc at Z.
- Taking Y and Z as centres and same radius, draw two arcs intersecting each other at S.
- Join OS and produce it to form a ray OB.
Thus, ∠BOA is required angle of 90.
(d) 120°
- Taking P as centre and same radius, cut previous arc at Q.
- Taking Q as centre and same radius cut the arc at S.
- Join OS.
Thus, ∠AOD is required angle of 120°.
- Taking X as centre and same radius, cut previous arc at Y.
- Taking Y as centre and same radius, draw another arc intersecting the same arc at Z.
- Taking Y and Z as centres and same radius, draw two arcs intersecting each other at S.
- Join OS and produce it to form a ray OB. Thus, ∠BOA is required angle of 90°.
- Draw the bisector of ∠BOA.
Thus, ∠MOA is required angle of 45°.
(f) 135°
- Draw a line PQ and take a point O on it.
- Taking O as centre and convenient radius, mark an arc, which intersects PQ at A and B.
- Taking A and B as centres and radius more than half of AB, draw two arcs intersecting each other at R.
- Join OR. Thus, ∠QOR = ∠POQ = 90° .
- Draw OD the bisector of ∠POR.
Thus, ∠QOD is required angle of 135°.
Question 6.
Draw an angle of measure 45° and bisect it.
Answer:
Steps of construction:
(a) Draw a line PQ and take a point O on it.
(b) Taking O as centre and a convenient radius, draw an arc which intersects PQ at two points A and B.
(c) Taking A and B as centres and radius more than half of AB, draw two arcs which intersect each other at C.
Question 7.
Draw an angle of measure 135° and bisect it.
Answer:
Steps of construction:
(a) Draw a line PQ and take a point O on it.
(b) Taking O as centre and convenient radius, mark an arc, which intersects PQ at A and B.
(c) Taking A and B as centres and radius more than half of AB, draw two arcs intersecting each other at R.
Question 8.
Draw an angle of 70°. Make a copy of it using only a straight edge and compasses.
Answer:
Steps of construction:
Step I: Draw a line 1 and mark a point O on it.
Step II: Using a protractor construct ∠AOB = 70°.
Step VI: With centre R and radius equal to EF, draw an arc intersecting the previous arc at S.
Step VII: Join PS and produce it.
Question 9.
Draw an angle of 40° Copy its supplementary angle.
Answer:
Steps of construction:
Step I: (a) By using protractor draw ∠AOB = 40°
∠COF is the supplementary angle.
Step V: With centre L and radius equal to EF draw an arc which intersects the previous arc at S.
Step VI: Join QS and produce it.
Thus, ZPQS is the copy of the supplementary angle ZCOB.
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