MP Board Class 6th Maths Solutions Chapter 14 Practical Geometry Ex 14.6
MP Board Class 6th Maths Solutions Chapter 14 Practical Geometry Ex 14.6
MP Board Class 6th Maths Solutions Chapter 14 Practical Geometry Ex 14.6
Question 1.
Draw ∠POQ of measure 75° and find its line of symmetry.
Solution:
Steps of construction :
(i) Draw a line l and mark a point O on it.
(ii) Place the pointer of the compasses at O and draw an arc of any radius which intersects the line l at Q.
(iii) Taking same radius, with centre Q, draw an arc which cuts the previous arc at B.
(iv) Join OB, then ∠BOQ = 60°.
(v) Taking same radius, with centre B, draw an arc which cuts the arc drawn in step
(ii) at C.
(vii) Draw OP as bisector of ∠DOB. Thus, ∠POQ = 75°.
Question 2.
Draw an angle of measure 147° and construct its bisector.
Solution:
Steps of construction :
Question 3.
Draw a right angle and construct its bisector.
Solution:
Steps of construction :
Question 4.
Draw an angle of measure 153° and divide it into four equal parts.
Solution:
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°
Solution:
Steps of construction:
(a) 60°
(iii) Taking P as centre and same radius, draw an arc which cut the previous arc at Q.
(iv) Join OQ and produce it to B. Thus, ∠BOA is the required angle of 60°.
(b) 30°
(iii) Taking P as centre and same radius, draw an arc which cut the previous arc at Q.
(iv) Join OQ and produce it to B. Thus, ∠BOA is the angle of 60°.
(v) Taking P as centre and radius more than half of PQ, draw an arc.
(vi) Taking Q as centre and with same radius, draw an arc which cut the previous arc at C.
(vii) Join OC. Thus ∠COA is the required angle of 30°.
(c) 90°
(iii) Taking X as centre and same radius, draw an arc which cut the previous arc at Y.
(iv) Taking Y as centre and same radius, draw another arc intersecting the arc drawn in step (ii) at ∠.
(v) Taking Y and ∠ as centres and same radius, draw two arcs intersecting each other at S.
(vi) Join OS and produce it to form a ray OB. Thus, ∠BOA is required angle of 90°.
(d) 120°
(iii) Taking P as centre and same radius, draw an arc which cut the previous arc at Q.
(iv) Taking Q as centre and same radius draw another arc intersecting the arc drawn in step (ii) at S.
(v) Join OS and produce it to D.
Thus, ∠AOD is the required angle of 120°.
(e) 45°
(iii) Taking X as centre and same radius, draw an arc which cut the previous arc at Y.
(iv) Taking Y as centre and same radius, draw another arc intersecting the arc drawn in step (ii) at Z.
(v) Taking Y and Z as centres and same radius, draw two arcs intersecting each other at S.
(vi) Join OS and produce it to B. Thus, ∠BOA is the angle of 90°.
(vii) Draw OM the bisector of ∠BOA.
Thus, ∠MOA is the required angle of 45°.
(f) 135°
Question 6.
Draw an angle of measure 45° and bisect it.
Solution:
Steps of construction :
Question 7.
Draw an angle of measure 135° and bisect it.
Solution:
Steps of construction :
Question 8.
Draw an angle of 70°. Make a copy of it using only a straight edge and compasses.
Solution:
Steps of construction:
(iii) Place the compasses at O and draw an arc to cut the rays of ∠POQ at L and M.
(iv) Use the same compasses setting to draw an arc with A as centre, cutting AB at X.
(v) Set your compasses setting to the length LM with the same radius.
(vi) Place the compasses pointer at X and draw the arc to cut the arc drawn earlier at Y.
(vii) Join AY.
Thus, ∠YAX = 70°.
Question 9.
Draw an angle of 40°. Copy its supplementary angle.
Solution:
Steps of construction :
(i) Draw an angle of 40° with the help of protractor, i.e., ∠AOB = 40°.
(iii) Take any point M on PQ.
(iv) Place the compasses at O and draw an arc to cut the rays of ∠AOB at L and N.
(v) Use the same compasses setting to draw an arc M as centre, cutting MQ at X.
(vi) Set your compasses to length LN with the same radius.
(vii) Place the compasses at X and draw the arc to cut the arc drawn earlier at Y.
(viii) Join MY.
(ix) Thus, ∠QMY = 40° and ∠PMY is supplementary of it.
MP Board Class 6th Maths Solutions
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