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

Question 12 Marks
Two straight lines are cut by a transversal so that the co-interior angles are equal. What must be the measure of each interior angle to make the straight lines parallel to each other?
Answer
A transveral intersects two straight lines and co-interior angles are equal to each other,
∵ The two straight lines are parallel Their sum of co-interior angles = 180°
But both angles are equal
$\therefore$ Each angle will be $\frac{180^{\circ}}{2}=90^{\circ}$
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Question 22 Marks
Draw ∠PQR = 75° by using set- squares. On PQ mark a point M such that MQ = 3 cm. On QR mark a point N such that QN = 4 cm. Join M and N. Measure the length of MN.
Answer

Length of MN = 4.3 cm
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Question 32 Marks
Draw ∠ABC = 120°. Bisect the angle using ruler and compasses. Measure each angle so obtained and check whether or not the new angles obtained on bisecting ∠ABC are equal.
Answer

Measuring PQ = 60°
Yes, angles obtained in ∠ABC bisecting are equal.
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Question 42 Marks
Draw a line segment OP = 8cm. Use set-square to construct ∠POQ = 90°; such that OQ = 6 cm. Join P and Q; then measure the length of PQ.
Answer

Measuring PQ = 10 cm
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Question 52 Marks
Draw a line segment OA = 5 cm. Use set-square to construct angle AOB = 60°, such that OB = 3 cm. Join A and B; then measure the length of AB.
Answer
Measuring the length of AB = 4.4cm. (approximately)
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Question 62 Marks
Construct the 45° angle, using ruler and a pair of compass only.
Answer
Draw an angle of 90° as in the previous question and bisects it. Each angle so obtained will be 45°.
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Question 72 Marks
Find x, y and z in the figure given below:
Answer
x = 180 - 75 = 105°   [Co-interior angles]
y = 180 - x                  [Co-interior angles]
= 180 - 105 = 75°
z = 75°                        [Co-interior angles]
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Question 82 Marks
Find a, b, c and d in the figure given below:
Answer
a = 130°    [Vertically of angles]
b = 150°      [vertically opposite Angles]
c = 150°      [Alternate interior angles] 
d = 130°    [Alternate interior angles]
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Question 92 Marks
In the given figure, find the angles shown by x,y, z and w. Give reasons.
Answer
x = 115°    [Vertically of angles]
y = 70°      [vertically opposite Angles]
z = 70°      [Alternate interior angles] 
w = 115°    [Alternate interior angles]
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Question 102 Marks
The figure given below shows a pair of parallel lines cut by a transversal for the following case, find a and b, giving reason.
Answer
a = 180° - 90°     (Linear pairs of angles)
= 90°
b = 90°     (Corresponding angles)
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Question 132 Marks
The figure given below shows a pair of parallel lines cut by a transversal for the following case, find a and b, giving reason.
Answer
a = 72°     (Alternate interior angles)
b = a     (Vertically opposite angles)
i.e. b = 72°
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Question 142 Marks
The figure given below shows a pair of parallel lines cut by a transversal for the following case, find a and b, giving reason.
Answer
a = 60°     (Alternate interior angles)
b = 180° - a     (Co-interior angles)
= 180° - 60° = 120°
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Question 152 Marks
The figure given below shows a pair of parallel lines cut by a transversal for the following case, find a and b, giving reason.
Answer
∵ l || m and p intersects them
b + 60° = 180°     (Linear pair)
∴ b = 180° - 60° = 120°
and a = 60°    (corresponding angle)
∴ a = 60°, b = 120°
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[2 Mark Question Answer] - MATHS STD 6 Questions - Vidyadip