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Maths 2 Mark Question

Constructions · Maharashtra Board STD 9 (MSBSHSE - English Medium). 12 questions.

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2 Mark Question

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12 questions · self-marked practice — reveal the answer and mark yourself.

Question 12 Marks
Draw a pair of vertically opposite angles. Bisect each of the two angles. Verify that the bisecting rays are in the same line.
Answer

Steps of construction:
  1. Draw a pair of vertically opposite angle $\angle\text{AOC}$ and $\angle\text{DOB}.$
  2. Keeping O as the centre and any radius draw two arcs which intersect OA at P, OC at Q, OB at S and OD at R.
  3. Keeping P and Q as centre and radius more than half of PQ draw two arcs which intersect each other at T.
  4. Join TO.
  5. Keeping R and S as centre and radius more than half of RS draw two arcs which intersect each other at U.
  6. Join OU.
Therefore TOU is a straight line.
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Question 22 Marks
Using the protractor, draw a right angle. Bisect it to get an angle of measure 45°.
Answer

Steps of construction:
  1. Draw an angle ABC of 90°.
  2. With B as the centre and any radius draw an arc which intersects AB at P and BC at Q.
  3. With P as center and radius more than half of PQ draw an arc.
  4. With Q as center and same radius draw an arc which intersects the previous arc at R.
  5. Join RB.
Therefore $\angle\text{RBC}=45^\circ$
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Question 32 Marks
Construct the following angles at the initial point of a given ray and justify the construction:
  1. 45°
  2. 90°
Answer

  1. Steps of construction:
  1. Draw a line segment AB and produce BA to C.
  2. Keeping A as the center and any radius draw an arc which intersects AC at D and AB at E
  3. Keeping D and E as center and radius more than half of DE draw arcs which intersect each other at F.
  4. Join FA which intersects the arc in (2) at G.
  5. Keeping G and E as center and radius more than half of GE draw arcs which intersect each other at H.
  6. Join HA.
Therefore $\angle\text{HBC}=45^\circ$
  1. Steps of construction
  1. Draw a line segment AB.
  2. Keeping A as the center and any radius draw an arc which intersects AB at C.
  3. Keeping C as center and the same radius draw an arc which intersects the previous arc at D.
  4. Keeping D as the center and same radius draw an arc which intersects arc in (2) at E.
  5. Keeping E and D as center and radius more than half of ED draw arcs which intersect each other at F.
  6. Join FA.
Therefore $\angle\text{FAB}=90^\circ$
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Question 42 Marks
Construct the angles of the following measurements:
105°
Answer

Steps of construction:
  1. Draw a line segment AB.
  2. Keeping A as the centre and any radius draw an arc which intersects AB at C.
  3. Keeping C as centre and the same radius draw an arc which intersects the previous arc at D.
  4. Keeping D as the centre and same radius draw an arc which intersects arc in (2) at E.
  5. Keeping E and D as centre and radius more than half of ED draw arcs which intersect each other at F.
  6. Join FA which intersects arc in (2) at G.
  7. Keeping E and G as center and radius more than half of EG draw arcs which intersect each other at H.
  8. Join HA.
Therefore $\angle\text{HAB}=105^\circ $
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Question 52 Marks
Draw an obtuse angle. Bisect it. Measure each of the angles so obtained.
Answer

Steps of construction:
  1. Draw an angle $\angle\text{ABC}$ of 120°.
  2. With B as a centre and any radius, draw an arc which intersects AB at P and BC at Q.
  3. With P as center and radius more than half of PQ draw an arc.
  4. With Q as a center and same radius draw an arc which cuts the previous arc at R.
  5. Join BR.
Therefore $\angle\text{ABR}=\angle\text{RBC} =60^\circ$
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Question 62 Marks
Draw a linear pair of angles. Bisect each of the two angles. Verify that the two bisecting rays are perpendicular to each other.
Answer

Steps of construction:
  1. Draw two angles DCA and DCB forming linear pair.
  2. With center C and any radius draw an arc which intersects AC at P and CD at Q and CB at R.
  3. With center P and Q and any radius draw two arcs which intersect each other at S.
  4. Join SC.
  5. With Q and R as center and any radius draw two arcs which intersect each other at T.
  6. Join TC.
Therefore $\angle\text{SCT}=90^\circ$
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Question 72 Marks
Construct the angles of the following measurements:
75°
Answer

Steps of construction:
  1. Draw a line segment AB.
  2. Keeping A as centre and any radius draw an arc which intersects AB at C.
  3. Keeping C as centre and the same radius draw an arc which intersects the previous arc at D.
  4. Keeping D as centre and same radius draw an arc which intersects arc in (2) at E.
  5. Keeping E and D as centre and radius more than half of ED, draw arcs intersecting each other at F.
  6. Join FA which intersects arc in (2) at G.
  7. Keeping G and D as centre and radius more than half of GD draw arcs intersecting each other at H.
  8. Join HA.
Therefore $\angle\text{HAB}=75^\circ $
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Question 82 Marks
Construct the angles of the following measurements:$22\frac{1^\circ}{2}$
Answer

Steps of construction:
  1. Draw a line segment AB.
  2. Keeping A as the centre and any radius draw an arc which intersects AB at C.
  3. Keeping C as centre and the same radius draw an arc which intersects the previous arc at D.
  4. Keeping D as the centre and same radius draw an arc which intersects arc in (2) at E.
  5. Keeping E and D as centre and radius more than half of ED draw arcs which intersect each at F.
  6. Join FA which intersects arc in (2) at G.
  7. Keeping G and C as centre and radius more than half of GC draw arcs intersecting each other at point H.
  8. Join HA which intersects the arc in (2) at a point I.
  9. Keeping I and C as centre and radius more than half of IC draw arcs intersecting each other at point J.
  10. Join JA.
Therefore $\angle\text{JAB}=22\frac{1^\circ}{2}$
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Question 92 Marks
Draw an angle and label it as $\angle\text{BAC}.$ Construct another angle, equal to $\angle\text{BAC}.$
Answer


Steps of construction:
  1. Draw an angle ABC and a line segment QR.
  2. With center A and any radius, draw an arc which intersects $\angle\text{BAC}$ at E and D.
  3. With Q as a centre and same radius draw an arc which intersects QR at S.
  4. With S as center and radius equal to DE, draw an arc which intersects the previous arc at T.
  5. Draw a line segment joining Q and T.
Therefore $\angle\text{PQR}=\angle\text{BAC} $
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Question 102 Marks
Construct the angles of the following measurements:
30°
Answer

Steps of construction:
  1. Draw a line segment AB.
  2. Keeping A as the centre and any radius draw an arc which intersects AB at C.
  3. Keeping C as center and the same radius draw an arc which intersects the previous arc at D.
  4. Keeping D and C as center and radius more than half of DC draw arcs which intersect each other at E.
  5. Join EA.
Therefore $\angle\text{EAB}=30^\circ $
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Question 112 Marks
Using your protractor, draw an angle of measure 108°. With this given angle as given, draw an angle of 54°.
Answer

Steps of construction:
  1. Draw an angle ABC of 108°.
  2. With B as the center and any radius draw an arc which intersects AB at P and BC at Q.
  3. With P as center and radius more than half of PQ draw an arc.
  4. With Q as the centre and same radius draw an arc which intersects the previous arc at R.
  5. Join BR.
Therefore $\angle\text{RBC}=60^\circ$
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Question 122 Marks
Construct the angles of the following measurements:
15°
Answer

Steps of construction:
  1. Draw a line segment AB.
  2. Keeping A as the centre and any radius draw an arc which intersects AB at C.
  3. Keeping C as centre and the same radius draw an arc which intersects the previous arc at D
  4. Keeping D and C as centre and radius more than half of DC draw arcs which intersect each other at E.
  5. Join EA which intersects arc in (2) at F.
  6. Keeping F and C as centre and radius more than half of FC draw arcs which intersect each other at G.
  7. Join GA.
Therefore $\angle\text{GAB}=15^\circ $
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