Exercise 14.1Exercise 14.2Exercise 14.3Exercise 14.4Exercise 14.5Exercise 14.6 |

**NCERT Answers for Class 6 Maths**

Chapter 14 Practical Geometry Exercise 14.6

Chapter 14 Practical Geometry Exercise 14.6

**Page 291**

**Ex 14.6 Class 6 Maths Question 1. Draw ∠ POQ of measure 75° and find its line of symmetry.**

**Answer**

**Step 1:** Draw a line I and mark a point O on it.

**Step 2:** Place the pointer of the compasses at O and draw an arc of any radius which intersects the line I at A.

**Step 3: **Taking same radius, with centre A, cut the previous arc at B.

**Step 4: **Join 0B, then ∠ BOA = 60°.

**Step 5: ** Taking same radius, with centre B, cut the previous arc at C.

**Step 6: **Draw bisector of ∠ BOC. The angle is of 90°. Mark it at D. Thus, ∠ DOA = 90°

**Step 7: **Draw OP as bisector of Z DOB. Thus, ∠ POA= 75°

**Ex 14.6 Class 6 Maths Question 2. Draw an angle of measure 147° and construct its bisector.
**

**Answer**

**Step 1:** Draw a ray **OA**

**Step 2:** With the help of protractor, construct ∠ AOB = 147°.

**Step 3:** Taking centre O and any convenient radius, draw an arc which intersects the arms **OA **and **OB **at P and Q respectively.

**Step 4:** Taking P as centre and radius more than half of PQ, draw an arc.

**Step 5:** Taking Q as centre and with the same radius, draw another arc which intersects the previous at R.

**Step 6:** Join OR and produce it.

**Step 7:** Thus, **OR **is the required bisector of ∠ AOB.

**Ex 14.6 Class 6 Maths Question 3. Draw a right angle and construct its bisector.
**

**Answer**

Steps of construction:

**Step 1:** Draw a line PQ and take a point O on it.

**Step 2:** Taking O as centre and convenient radius, draw an arc which intersects PQ at A and B.

**Step 3:** Taking A and B as centres and radius more than half of AB, draw two arcs which intersect each other at C.

**Step 4:** Join OC. Thus, ∠ COQ is the required right angle.

**Step 5:** Taking B and E as centre and radius more than half of BE, draw two arcs which intersect each other at the point D.

**Step 6:** Join OD . Thus, **OD** is the required bisector of ∠ COQ.

**Ex 14.6 Class 6 Maths Question 4. Draw an angle of measure 153° and divide it into four equal parts.**

**Answer**

Steps of construction:

**Step 1:** Draw a ray **OA** .

**Step 2:** At O, with the help of a protractor, construct ∠ AOB = 153°

**Step 3:** Draw **OC** as the bisector of ∠ AOB.

**Step 4:** Again, draw **OD **as bisector of ∠ AOC.

**Step 5:** Again, draw **OE** as bisector of ∠ BOC.

**Step 6:** Thus, **OC**, **OD **and **OE **divide ∠ AOB in four equal parts.

**Ex 14.6 Class 6 Maths Question 5. Construct with ruler and compasses, angles of following measures: (a) 60° (b) 30° (c) 90° (d) 120° (e) 45° (f) 135°**

**Answer**

**(a) 60°
**

**Step 1:** Draw a ray **OA**

**Step 2:** Taking O as centre and convenient radius, mark an arc, which intersects OA at P.

**Step 3:** Taking P as centre and same radius, cut previous arc at Q.

**Step 4:** Join OQ. Thus, ∠ BOA is required angle of 60**°**.

**(b) 30°**

**Step 1:** Draw a ray OA

**Step 2:** Taking O as centre and convenient radius, mark an arc, which intersects OA at P.

**Step 3: **Taking P as centre and same radius, cut previous arc at Q.

**Step 4: **Join OQ. Thus, ∠ BOA is required angle of 60**°**

**Step 5: **Put the pointer on P and mark an arc.

**Step 6: **Put the pointer on Q and with same radius, cut the previous arc at C.

**Step 7: **Thus, ∠ COA is required angle of 30**°**.

**(c) 90°**

**Step 1:** Draw a ray OA.

**Step 2:** Taking O as centre and convenient radius, mark an arc, which intersects OA at X.

**Step 3:** Taking X as centre and same radius, cut previous arc at Y.

**Step 4:**Taking Y as centre and same radius, draw another arc intersecting the same arc at Z.

**Step 4:** Join OS and produce it to form a ray OB.

Thus, ∠ BOA is required angle of 90°

**(d) 120°**

**Step 1:** Draw a ray OA

**Step 2:** Taking O as centre and convenient radius, mark an arc, which intersects OA at P.

**Step 3:** Taking P as centre and same radius, cut previous arc at Q.

**Step 4:** Taking Q as centre and same radius cut the arc at S. Join OS.

Thus, ∠ AOD is required angle of 120°

**(e) 45°**

**Step 1:** Draw a ray OA.

**Step 2:** Taking O as centre and convenient radius, mark an arc, which intersects OA at X.

**Step 3:** Taking X as centre and same radius, cut previous arc at Y

**Step 4:** Taking Y as centre and same radius, draw another arc intersecting the same arc at Z.

**Step 5:** Taking Y and Z as centres and same radius, draw two arcs intersecting each other at S.

**Step 5:** Join OS and produce it to form a ray OB. Thus, ∠ BOA is required angle of 90°

**Step 6:** Draw the bisector of ∠ BOA. Thus, ∠ MOA is required angle of 45°

**(f) 135°**

**Step 1:** Draw a line PQ and take a point O on it.

**Step 2:** Taking O as centre and convenient radius, mark an arc, which intersects PQ at A

**Step 3: **Taking A and B as centres and radius more than half of AB, draw two arcs intersecting each other at R.

**Step 4: **Join OR. Thus, ∠ QOR= ∠POQ = 90°

**Step 5: **Draw OD the bisector of ∠ POR.

Thus, ∠ QOD is required angle of 135°

**Ex 14.6 Class 6 Maths Question 6. Draw an angle of measure 45° and bisect it.**

**Answer**

Steps of construction:

**Step 1:** Draw a line PQ and take a point O on it.

**Step 2:** Taking O as centre and a convenient radius, draw an arc which intersects PQ at two points A and B.

**Step 3:** Taking A and B as centres and radius more than half of AB, draw two arcs which intersect each other at C.

**Step 4:** Join OC. Then ∠ COQ is an angle of 90°

**Step 5:** Draw OE as the bisector of ∠ COE. Thus, ∠ QOE = 45°

**Step 6:** Again draw OG as the bisector of ∠ QOE. Thus, ∠ QOG = ∠ EOG = 22½°

**Ex 14.6 Class 6 Maths Question 7. Draw an angle of measure 135° and bisect it.**

**Answer**

Steps of construction:

**Step 1:** Draw a line PQ and take a point O on it.

**Step 2:** Taking O as centre and convenient radius, mark an arc, which intersects PQ at A and B.

**Step 3:** Taking A and B as centres and radius more than half of AB, draw two arcs intersecting each other at R. Join OR.

**Step 4:** Thus, ∠ QOR= ∠ POQ= 90°

**Step 5:** Draw OD the bisector of ∠ POR.

Thus, ∠ QOD is required angle of 135°

**Step 6:** Now, draw OE as the bisector of ∠ QOD.

Thus, ∠ QOE = ∠ DOE = 67½°

**Ex 14.6 Class 6 Maths Question 8. Draw an angle of 70 ^{O}. Make a copy of it using only a straight edge and compasses.**

**Answer**

Steps of construction:

Draw an angle 700 with protractor, i.e., ∠POQ = 70°

Draw a ray AB.

Place the compasses at O and draw an arc to cut the rays of ∠ POQ at L and M.

Use the same compasses, setting to draw an arc with A as centre, cutting AB at X.

Set your compasses setting to the length LM with the same radius.

Place the compasses pointer at X and draw the arc to cut the arc drawn earlier at Y.

Join AY. Thus, ∠ YAX= 70°

**Ex 14.6 Class 6 Maths Question 9. Draw an angle of 40 ^{O}. Copy its supplementary angle.**

**Answer**

Steps of construction:

(a) Draw an angle of 40° with the help of protractor, naming ∠ AOB.

Draw a line PQ.

Take any point M on PQ.

Place the compasses at O and draw an arc to cut the rays of ∠ AOB at L and N.

Use the same compasses setting to draw an arc M as centre, cutting MQ at X.

Set your compasses to length LN with the same radius.

Place the compasses at X and draw the arc to cut the arc drawn earlier Y.

Join MY. Thus, ∠ QMY = 40° and ∠ PMY is supplementary of it.

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