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MATHS [3 marks sum]

Properties of Angles and Lines (Including Parallel Lines) · ICSE STD 6 (ICSE - English Medium). 14 questions.

Questions

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Question 13 Marks
Draw a line segment BC = 8 cm. Using set-squares, draw ∠CBA = 60° and ∠BCA = 75°. Measure the angle BAC. Also measure the lengths of AB and AC.
Answer

Length AB = 11 cm
Length AC = 9.8 cm
∠BAC = 45°.
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Question 23 Marks
In the case, given below, draw perpendicular to AB from an exterior point P.
Answer

Steps of construction:
  1. From point P, draw an arc CD at line AB.
  2. From point C and D draw arcs that intersect each other at point E, now draw PE, perpendicular to AB.
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Question 33 Marks
In the case, given below, draw perpendicular to AB from an exterior point P.
Answer

Steps of Construction:
  1. From point P, draw an arc CD at line AB
  2. From point C and D draw arcs that intersect each other at point E, now draw PE, perpendicular to AB.
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Question 43 Marks
In the case given below, find the value of x so that POQ is straight line
Answer
5.5x + 15° = 180°
⇒ 5.5x = 180° - 15°
⇒ 5.5x = 165°
$\Rightarrow \frac{18 x }{11}=180^{\circ}$
$\Rightarrow x=\frac{165}{5.5}=\frac{165 \times 10}{55}=30^{\circ}$
\∴ x = 30°
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Question 53 Marks
In the case given below, find the value of $x$ so that $\text{POQ}$ is straight lin
Answer
$\because \text{POQ}$ is a straight line
$\therefore \angle \text{POL} + \angle \text{LOQ} = 180^\circ$
$\Rightarrow \frac{7 x}{11}+x=180^{\circ}$
$\Rightarrow \frac{7 x+11 x}{11}=180^{\circ}$
$\Rightarrow \frac{18 x}{11}=180^{\circ}$
$\Rightarrow x=\frac{180^{\circ} \times 11}{18}=110^{\circ}$
$\therefore x = 110^\circ$
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Question 63 Marks
Without using set squares, construct angle ABC = 60° in which AB = BC = 5 cm. Join A and C and measure the length of AC.
Answer
Steps of Construction:
  1. Draw an angle ABC = 60
    Such that AB = BC = 5 cm
  2. Join AC, on measuring, the length of AC = 5 cm.
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Question 73 Marks
Using the given figure, fill in the blanks.
∠x = _______; ∠z = ___________;
∠p = _______; ∠q = __________;
∠r = _______; ∠s = ___________;
Answer
x = 60° [Corresponding angles]
z = x    [Corresponding angles]
= 60°
p = z    [Vertically opposite angle]
= 60°
q = 180 - P   [Linear Pair of angles]
= 180 - 60 = 120°
r = 180 - x    [Linear Pair of angles]
= 180 - 60 = 120°
s = r    [Vertically opposite angle] = 120°
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Question 83 Marks
In the figure given below, find the measure of the angles denoted by x,y, z,p,q and r.
Answer
x = 180 - 100  [L.P. of angles] = 80°
y = x  [Alternate exterior angles]
= 80°
z = 100°     [Corresponding angles]
p = x        [Vertically opp. angles]
= 80°
q = 100°   [Vertically opp. angles]
r = q        [Corresponding angles]
= 100°
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Question 93 Marks
Identify the pair of angles in the figure given below :
adjacent angles, vertically opposite angles, interior alternate angles, corresponding angles or exterior alternate angles.
  1. ∠1 and ∠10
  2. ∠6 and ∠12
  3. ∠8 and ∠10
  4. ∠4 and ∠11
  5. ∠2 and ∠8
  6. ∠5 and ∠7
Answer
  1. Corresponding
  2. Alternate exterior
  3. Alternate interior
  4. Alternate interior
  5. Alternate exterior
  6. Vertically opposite
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Question 103 Marks
Identify the pair of angles in the figure given below :
adjacent angles, vertically opposite angles, interior alternate angles, corresponding angles or exterior alternate angles.
  1. ∠2 and ∠7
  2. ∠4 and ∠8
  3. ∠1 and ∠8
  4. ∠1 and ∠5
  5. ∠4 and ∠7
Answer
  1. Alternate interior angles
  2. Corresponding angles
  3. Alternate exterior angles
  4. Corresponding angles
  5. Allied angles
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Question 113 Marks
Identify the pair of angles in the figure given below :
adjacent angles, vertically opposite angles, interior alternate angles, corresponding angles or exterior alternate angles.
  1. ∠2 and ∠4
  2. ∠1 and ∠8
  3. ∠4 and ∠5
  4. ∠1 and ∠5
  5. ∠3 and ∠5
Answer
  1. Adjacent angles
  2. Alternate exterior angles
  3. Interior alternate angles
  4. Corresponding angles
  5. Allied angles
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Question 123 Marks
The figure given below shows a pair of adjacent angles AOB and BOC. Find whether or not the exterior arms OA and OC are in the same straight line
Answer
∠AOB + ∠COB = 180°
Since, the sum of adjacent angles AOB and COB = 180°
(90° -x) + (90°+ x) = 180°
⇒ 90°-x + 90° + x = 180°
⇒ 180° =180°

The exterior arms. OA and OC are in the same straight line.

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Question 133 Marks
The given diagram, shows two adjacent angles AOB and AOC, whose exterior sides are along the same straight line. Find the value of x
Answer
Since, the exterior arms of the adjacent angles are in a straight line ; the adjacent
angles are supplementary
∴ ∠AOB + ∠AOC = 180°
⇒ 68° + 3x – 20° = 180°
⇒ 3x = 180° + 20° – 68°
⇒ 3x = 200° – 68° ⇒ 3x =132°
x = 132/3° = 44°
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Question 143 Marks
Two straight lines AB and CD intersect each other at a point O and angle AOC = 50° ; find:
(i) angle BOD
(ii) ∠AOD
(iii) ∠BOC
Answer
(i)∠BOD = ∠AOC
(Vertically opposite angles are equal)
∴ ∠BOD =50°
(ii) ∠AOD
∠AOD + ∠BOD = 180°
∠AOD + 50° = 180° [From (i)]
∠AOD = 180°-50°
∠AOD = 130°
(iii) ∠BOC = ∠AOD
(Vertically opposite angles are equal)
∴ ∠BOC =130°
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[3 marks sum] - MATHS STD 6 Questions - Vidyadip