Lines And Angles Test

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Lines And Angles Test - 7

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Weekly Quiz Competition

Question 1
1 / -0

Which of the following statements is not true?

A
A straight line has neither a start point nor an end point, and is of infinite length.

B
An angle that measures between 90° and 180° is called an obtuse angle.

C
If the sum of two angles is 90°, then the two angles are called complementary angles.

D
The angles that have a common arm and a common vertex are called vertically opposite angles.

Solution

The angles that have a common arm and a common vertex are called adjacent angles.
In the figure below, BOA and AOC are adjacent angles. Their common arm is OA and common vertex is O.
Question 2
1 / -0

In the figure given below, P and Q are parallel lines. Which of the following option is false based on the figure?

A
1 + 2 = 5 + 6

B
2 + 3 = 5 + 8

C
2 + 4 = 6 + 8

D
1 + 7 = 2 + 4

Solution

1 + 2 = 5 + 6 (Both are linear pairs.)
We have:
2 + 3 = 5 + 8 (Both are linear pairs.)
2 = 6 (Corresponding angles)
4 = 8 (Corresponding angles)
So, 2 + 4 = 6 + 8
1 + 7 ≠ 2 + 4
So, this is incorrect.
Question 3
1 / -0

Which of the lines given in the options is perpendicular to line AB?

A
PQ

B
EF

C
CD

D
GH

Solution

Perpendicular lines: When there is a right angle between two lines, the lines are said to be perpendicular to each other.
Here, AB ⊥ CD
Question 4
1 / -0

Find x in the given figure, if DC is parallel to MN.

A
45°

B
40°

C
37°

D
22°

Solution

From the given figure, we notice that:
AOC = DOM = 34°(Vertically opposite angles)
Also,
DOM = NMB = 34° (NM ∥ DC, Corresponding angles)
So, we have:
12° + x = 34°x = 34° - 12°x = 22°
Question 5
1 / -0

Find the value of 'x', if m || n.

A
50°

B
60°

C
100°

D
110°

Solution

Draw a line p || m || n.
Now, x° = (a + b)°
a = 60°[Alternate interior angles]
b = 50° [Alternate interior angles]
So, x° = (60 + 50)° = 110°
Question 6
1 / -0

Find the missing angles (p and q) in the following figure:

A
p = 34°, q = 55°

B
p = 40°, q = 60°

C
p = 42°, q = 65°

D
p = 48°, q = 70°

Solution

Here, angle C is a straight angle, i.e. 180°.
Now, p + 32° + 24° = 90°
56° + p = 90°
p = 90° - 56° = 34°
Now, 35° + q = 90°
q = 90° - 35° = 55°
Question 7
1 / -0

In the following figure (not drawn to scale), QER and QFP are straight lines. RQP is a right angle and EM | | QN | | FO. Find j.

A
49°

B
51°

C
56°

D
60°

Solution

Since FO II QN and QR is a transversal, therefore
REM = EQN (corresponding angles)
EQN = 39°
Now, RQF = 90° (given)
EQN + NQP = 90°QNP + 39° = 90°
QNP = 90° - 39°= 51°
Also, QN II FO and QP is a transversal, therefore
j = NQP (Corresponding angles)
j = 51°
Question 8
1 / -0

In the given figure, AB and CD are straight lines intersecting each other at O. EO is perpendicular to CD. Find the measures of FOB and EOG, respectively.

A
70° and 66°

B
70° and 77°

C
70° and 76°

D
67° and 66°

Solution

From the given information:
EO is perpendicular to CD.
Hence,
EOG = 90°- 24°= 66°Also,
DOF + FOB + BOC = 180°70° + FOB + 40°= 180°FOB = 180° - 110°
FOB = 70°
Question 9
1 / -0

In the diagram given below, FE and CD are two lines perpendicular to each other. What is the measure of a + b + e?

A
155°

B
150°

C
145°

D
140°

Solution

From the given information:
35° + e = 90°This gives e = 90°- 35°e = 55°d = 90°- 55° = 35°Also, d = a = 35° (vertically opposite angles)
And, e = b = 55° (vertically opposite angles)
So,
a + b + e = 35° + 55° + 55°= 145°
Question 10
1 / -0

In the given figure, if PQ || RS, what is the value of x?

A
70°

B
110°

C
100°

D
30°

Solution

As PQ || RS,
x + 70° = 180° [Co-interior angles]
x = 110°
Question 11
1 / -0

In the given figure, if AB ∥ KD and BN ∥ MV, then which of the following is false?

A
b =c

B
e + c = 180⁰

C
a = d

D
b = f

Solution

b = c (alternate interior angles)

e + c = 180° (Linear pair)

a + b = c + d (alternate interior angles)

Also , b = c
Which gives:
a = d

From the figure, we can clearly see that b ≠ f.
So, option 4 is false.
Question 12
1 / -0

What are the values of x, y and z in the given figure?

A
x = 118°, y = 32°, z = 30°

B
x = 128°, y = 30°, z = 32°

C
x = 95°, y = 32°, z = 53°

D
x = 118°, y = 32°, z = 35°

Solution

x + 30° + 32° = 180°
x = 180° - 62° = 118°
x = 118°
y = 32°(Vertically opposite angles)
z = 30°(Vertically opposite angles)
Question 13
1 / -0

In the given figure, WV is parallel to ST. In ∆STU, SUT = 90° and UTS = 51°. Find UWV.

A
39°

B
51°

C
90°

D
141°

Solution

WV is parallel to ST. (Given)
In ∆STU, SUT = 90° and UTS = 51°
So, SUT = WUV = 90° (Vertically opposite angles)
UTS = UWV (Alternate angles)
So,
51° + 90° + UVW = 180° (Sum of angles of a triangle)
UVW = 180° - 141°
UVW = 39°
Question 14
1 / -0

If || m || n and AB || DC, then what is the value of x?

A
105°

B
145°

C
125°

D
85°

Solution

1 = 2 as AB || CD
2 + 35° = 70° [Vertically opposite angles]
2 = 35°
∴ 1 = 35°
Now, x + 1 = 180° [Linear pair]
x = 180° - 35°
= 145°
Question 15
1 / -0

An equilateral triangle is drawn and the line from o is extended up to u, as shown below. If ypu = 60°, then find m.

A
60°

B
90°

C
100°

D
120°

Solution

An equilatral triangle has all three angles equal, with each measuring 60°. So, n = 60°.
60°+ m + 60°= 180° (Making a straight angle)
m = 180°- 120° m = 60°
Question 16
1 / -0

In the figure given below, if AB || CD, then find the measure of BGF.

A
60°

B
50°

C
70°

D
Data insufficient

Solution

It is given that AB || CD.
AMN = 70°
MND = 70°[Alternate interior angles]
END = 70° – 30° = 40°
Now, FEN + END = 140° + 40° = 180°
∴EF || CD [∵ Sum of adjacent angles is 180°, it means lines are parallel]
EF || AB
∠GFE = 50°
∴BGF = 50° [Alternate interior angles]
Question 17
1 / -0

If AB || CD and OP⊥AB, what is the value of x°?

A
90°

B
55°

C
125°

D
75°

Solution

PBQ = DQB= x [Alternate interior angles]
Also, 180°- DQB = 125°(Linear Pair)180° - x° = 125°x° = 180° - 125°x° = 55°
Question 18
1 / -0

In the given figure, AB || CD and EF is a transversal.

What is the measure of ?

A
74°

B
106°

C
116°

D
62°

Solution

x + 12° = 2x - 50° (Corresponding angles)
x = 62°
So, 2x - 50° = (2 × 62° - 50°) = 74°
Thus,
Question 19
1 / -0

In the figure, if PQ || RS, then what is the measure of XMY?

A
35°

B
40°

C
55°

D
60°

Solution

Introduce a line passing through M and parallel to PQ.

XMY = a + b
Now, a = PXM = 180° - 145° = 35°[Alternate interior angles]
b = 20°[Alternate interior angles]
∴ XMY = 55°
Question 20
1 / -0

If AB ∥ CD ∥ EF, then what is the measure of x?

A
70°

B
90°

C
100°

D
120°

Solution

We are given that:
AB ∥ CD, and BD is the transversal.
So,
45° = ABD (Alternate interior angles)
Also,
AB ∥ EF, and MF is the transversal.
So,
DMB = 35° (Alternate interior angles)

Now, in ΔMBD:
x + 35°+ 45° = 180°
x + 80° = 180°
x = 100°
Question 21
1 / -0

Fill in the blanks:

(A) Two lines that do not intersect each other at any point are called _________ lines.
(B) The shortest distance between two intersecting lines is ____________.
(C) The angles in each pair of corresponding angles are _________.
(D) A dot gives us an idea of a __________.

A
A - opposite
B - infinite
C - equal
D - point

B
A - parallel
B - zero
C - equal
D - point

C
A - parallel
B - zero
C - opposite
D - line

D
A - non-parallel
B - zero
C - not equal
D - point

Solution

(A) Two lines that do not intersect each other at any point are called parallel lines.
(B) The shortest distance between two intersecting lines is zero.
(C) The angles in each pair of corresponding angles are equal.
(D) A dot gives us an idea of a point.
Question 22
1 / -0

In the given figure, if AB || CD, then find the measure of y + 2z + x + 2m.

A
180°

B
200°

C
360°

D
230°

Solution

y = 32° (Vertically opposite angles)
Also,
y = x = 32° (Alternate interior angle angles)
Also,
y + z + m = 180°
Now, we need to measure y + 2z + x + 2m.
It can also be written as:
y + x + 2(z + m) = y + x + 2(180° - y)
= 32° + 32° + 2(180°- 32°) = 64° + 360° - 64° = 360°
Question 23
1 / -0

In the given figure, AB // CD.

Statement 1: x = 74° and y = 74°
Statement 2: z = 106°

Choose the correct option.

A
Both statements 1 and 2 are false.

B
Both statements 1 and 2 are true.

C
Only statement 1 is true.

D
Only statement 2 is true.

Solution

Statement 1: x = 74° (Alternate angles)
y = 74° (Corresponding angle with x)

Statement 2: z = 180° - 74° (Angles on a straight line)
z = 106°
Therefore, both the statements are true.
Question 24
1 / -0

In the given figure, AC = AB. AB is parallel to DF, BC is parallel to ED, AC is parallel to EF and CAB = 70°.

Find:
(i) 2x + y - z
(ii) x - y + z

A
(i) 55°
(ii) 70°

B
(i) 140°
(ii) 70°

C
(i) 70°
(ii) 70°

D
(i) 140°
(ii) 55°

Solution

ACB = ABC = (180° − 70°) ÷ 2 = 55° (ABC is an isosceles triangle.)
DAE = DFE = 70°
x = 70° (DF // AE and AD // EF)
So, AEFD is a parallelogram.
EBF = ∠EDF = 55°
y = 55°
(DF // EB and DE // FB)
So, DEBF is a parallelogram.
DCF = ∠DEF = 55°
z = 55°
(DE // CF and DC // EF)
So, DEFC is a parallelogram.
(i) 2x + y - z = 2(70°) + 55° - 55° = 140
(ii) x - y + z = 70° - 55° + 55° = 70°

Question 25

1 / -0

In the given figure, m and n are a pair of parallel lines.

Match the following based on the given figure:

Column - I	Column - II
(A) 2 = 4 6 = 8	(i) Corresponding angles
(B) 8 = 2 7 = 1	(ii) Vertically opposite angles
(C) 5 = 3 6 = 4	(iii) Alternate interior angles
(D) 6 = 2 4 = 8	(iv) Alternate exterior angles

A - (iii), B - (ii), C - (i), D - (iv)

A - (ii), B - (iv), C - (iii), D - (i)

A - (iv), B - (iii), C - (i), D - (ii)

A - (i), B - (iii), C - (ii), D - (iv)

Solution

(A) 2 = 4 and 6 = 8, as they are vertically opposite angles.
(B) 8 = 2 and 7 = 1, as they are alternate exterior angles.
(C) 5 = 3 and 6 = 4, as they are alternate interior angles.
(D) 6 = 2 and 4 = 8, as they are corresponding angles.
Hence, option 2 is correct.

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Re-Attempt Weekly Quiz Competition

Lines And Angles Test - 7

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Lines And Angles Test - 7

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SHARING IS CARING

Question 1

A straight line has neither a start point nor an end point, and is of infinite length.

An angle that measures between 90° and 180° is called an obtuse angle.

If the sum of two angles is 90°, then the two angles are called complementary angles.

The angles that have a common arm and a common vertex are called vertically opposite angles.

Solution

Question 2

1 + 2 = 5 + 6

2 + 3 = 5 + 8

2 + 4 = 6 + 8

1 + 7 = 2 + 4

Solution

Question 3

PQ

EF

CD

GH

Solution

Question 4

45°

40°

37°

22°

Solution

Question 5

50°

60°

100°

110°

Solution

Question 6

p = 34°, q = 55°

p = 40°, q = 60°

p = 42°, q = 65°

p = 48°, q = 70°

Solution

Question 7

49°

51°

56°

60°

Solution

Question 8

70° and 66°

70° and 77°

70° and 76°

67° and 66°

Solution

Question 9

155°

150°

145°

140°

Solution

Question 10

70°

110°

100°

30°

Solution

Question 11

b =c

e + c = 1800

a = d

b = f

Solution

Question 12

x = 118°, y = 32°, z = 30°

x = 128°, y = 30°, z = 32°

x = 95°, y = 32°, z = 53°

x = 118°, y = 32°, z = 35°

Solution

e + c = 180⁰

A - opposite
B - infinite
C - equal
D - point

A - parallel
B - zero
C - equal
D - point

A - parallel
B - zero
C - opposite
D - line

A - non-parallel
B - zero
C - not equal
D - point

(i) 55°
(ii) 70°

(i) 140°
(ii) 70°

(i) 70°
(ii) 70°