Lines And Angles Test

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Lines And Angles Test - 6

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Weekly Quiz Competition

Question 1
1 / -0

Which of the following statements is CORRECT?

A
Opposite angels of a parallelogram are congruent.

B
Each angle of an isosceles triangle is 60^o.

C
The sum of all angles of a square is 180^o.

D
Consecutive angles of a parallelogram are complementary.

Solution

Opposite angels of a parallelogram are congruent is correct.
In an isosceles triangle, only two angles are equal in value.
Sum of all angles of a square = 360^o
Consecutive angles of a parallelogram are supplementary.
Question 2
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In the following figure, lines PQ and RS cross each other as shown.

Which of the following options is true?

A
∠c =∠f

B
∠c = ∠e

C
∠c + ∠b = ∠d

D
∠a + ∠b = ∠d

Solution

∠a + ∠b =∠d is correct because of vertically opposite angles.
Question 3
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Which of the following lines is parallel to KL?

A
EF

B
CD

C
AB

D
GH

Solution

CD is parallel to KL.
Question 4
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If QS and PR are straight lines and ∠PON = 45^o, find the value of ∠NOS.

A
60^o

B
75^o

C
70^o

D
80^o

Solution

∠QOR = 115^o, which is equal to ∠POS (Vertically opposite angles)
∠POS = 45^o + ∠NOS = 115^o
∠NOS =115^o- 45^o
=> 70^o
Question 5
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If PQ is a straight line such that ∠POS = 90°. find the value of ∠c.

A
44°

B
31°

C
49°

D
51°

Solution

It can be seen from the figure that ∠POS = 90°.
So,
∠c + 46° = 90°∠c = 90°- 46°∠c = 44°
Question 6
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In the figure, there are 3 straight lines as shown. Find the value of ∠UOQ.

A
120^o

B
140^o

C
155^o

D
125^o

Solution

∠SOP + ∠POT + ∠ROT = 180^o (Straight line)
19^o+ ∠POT + 41^o = 180^o
∠POT = 180^o- 19^o- 41^o
∠POT = 120^o is vertically opposite to ∠UOQ.
So, ∠UOQ = 120^o
Question 7
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In the figure (not drawn to scale), ABC and CDF are two lines such that ACF is a right angle. If DG II CH II BI, find the value of angle 'x'.

A
25°

B
28°

C
30°

D
32°

Solution

Since BI II CH and AC is a transversal,
ABI = BCH (corresponding angles)
BCH = 60°
Now, ACF = 90° (given)
BCH + HCD = 90°
HCD + 60° = 90°
HCD = 90° - 60° = 30°
Also, CH II DG and CF is a transversal.
x = HCD (Corresponding angles)
x = 30°
Question 8
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In the figure (not drawn to scale), EFC and DFB are straight lines. Find the values of angles x and y, respectively.

A
125°, 75°

B
130°, 70°

C
135°, 65°

D
140°, 60°

Solution

(a) As ∠CFB + ∠x = 180° (Linear pair)
45° + ∠x = 180°
∠x = 180° - 45° = 135°
(b) As ∠y + ∠AFB + ∠BFC = 180° (Angles on a straight line)
∠y + 70° + 45° = 180°
∠y = 180° - (70° + 45°)
∠y = 180° - 115° = 65°
Question 9
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In the figure (not drawn to scale), AJE, BJF, CJG and DJH are straight lines. What is the value of angle x?

A
34^o

B
37^o

C
39^o

D
41^o

Solution

As ∠AJB + ∠BJC + ∠CJD + ∠DJE = 180⁰ (Angles on a straight line AE)
42^o + 59^o + 40^o + ∠y = 180^o
∠y = 180^o - (42^o + 59^o + 40^o)
∠y = 180^o - 141^o = 39^o

(b) ∠y = ∠x (Vertically opposite angles)
∠x = 39^o
Question 10
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In the figure, PQ is parallel to ST. AB is a straight line. Find the measure of ∠QSA.

A
22^o

B
24^o

C
26^o

D
28^o

Solution

Since PQ II ST
∠PQS = ∠QST (Alternate angles)
∠QST = 96^o
∠QSA + ∠AST = 96^o
∠QSA = 96^o - 70^o = 26^o
Question 11
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In the given figure, BC || ED and ∠AOC = 78^o.

Which of the following options is true?

A
∠AOB + 78^o = 180^o

B
∠AOB + ∠COE = 180^o

C
∠BOE + ∠BOC = 180^o

D
∠BOE + ∠OED = 180^o

Solution

Only the first option is true as it shows the linear pair
∠AOB + 78^o = 180^o
Question 12
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Three lines a, b and c are parallel to each other. A transversal x is drawn through them as shown. Another line d is drawn perpendicular to line c.

Which of the angles are corresponding to ∠2?

A
∠j, ∠6

B
∠4, ∠6

C
∠4, ∠l

D
∠m, ∠g

Solution

Corresponding Angles: The angles which occupy the same relative position at each intersection where a straight line crosses two others.
If the two lines are parallel, the corresponding angles are equal. So, ∠4 and ∠6 are corresponding to ∠2.
Question 13
1 / -0

In the given figure, PQ || ST. In ∆RPQ, ∠PRQ = 90^o and ∠RPQ = 64^o. Find the measure of ∠RTS.

A
68^o

B
65^o

C
64^o

D
60^o

Solution

Given: PQ || ST
In ∆RPQ,
∠PRQ = 90^o and ∠RPQ = 64^o
So, ∠PRQ = ∠SRT (Vertically opposite angles = 90^o)
∠RPQ = ∠RTS (Alternate angles = 64^o)
So, ∠RTS = 64^o
Question 14
1 / -0

Find the measure of angle marked as 1.

A
150^o

B
100^o

C
90^o

D
60^o

Solution

∠1+ ∠c = 180^o∠1+ 120^o= 180^o=> ∠1 = 60^o
Question 15
1 / -0

In the given figure, IH || OF, HB⊥AF, IH⊥HB and ∠1 = 65^o. Find the measure of ∠2.

A
115^o

B
116^o

C
117^o

D
118^o

Solution

Given: ∠1 = 65^o
∠HOG = 90^o
∠IHO = 90^o
∠2 = ?
In the quadrilateral,
∠1 + ∠HOG + ∠IHO +∠2 = 360^o
65^o + 90^o + 90^o + ∠2= 360^o
∠2 = 360^o- 245^o
∠2 = 115^o
Question 16
1 / -0

Find the measure of ∠1.

A
180°

B
120°

C
100°

D
90°

Solution

∠qop + ∠rop +∠rot = 180^o (Angles on a straight line)
∠rop =∠sou = 35^o
=> ∠1+ 35^o + 55^o = 180^o
=>∠1= 90^o
Question 17
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In the following figure, ∠OPQ = 78^o and ∠OQP = 65^o. Find the measure of ∠SOR.

A
36^o

B
37^o

C
38^o

D
39^o

Solution

Given: ∠OPQ = 78^o and ∠OQP = 65^o
So, in ∆POQ,
∠OPQ + ∠OQP + ∠POQ = 180°
180^o = 78^o + 65^o + ∠POQ
180^o - 143^o = ∠POQ
∠POQ = 37^o
So, ∠POQ = ∠SOR (Vertically opposite angles)
∠SOR = 37^o
Question 18
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In the given figure lv and mp are parallel lines and ro and nq are transverse. Find the value of ∠1,∠2 and ∠3.

A
83^o, 69^o, 80^o

B
69^o, 81^o, 69^o

C
111⁰,69⁰,69⁰

D
69⁰,69^o, 83^o

Solution

Since the parallel lines are intersected by a transverse,
∠mbc + ∠cba = 180⁰69^o+ ∠cba = 180⁰So ∠1 = 180^o- 69^o = 111^o^{Also we notice that:}∠2 = 69^o(vertically opposite angles)Now ∠mbc = ∠nba (vertically opposite angles)
Also
∠nba = ∠oap (corresponding angles).
Hence, ∠3 = 69^o.
Question 19
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Which of the following statements is/are correct?

Statement-1: Two equal angles on the same side of a line that crosses two parallel lines, and on the same side of each parallel line are called corresponding angles.

Statement-2: Two equal angles on opposite sides of a line that crosses two parallel lines, and on opposite sides of those lines are called alternate interior angles.

A
Only statement-1 is correct.

B
Only statement-2 is correct.

C
Both statements are correct.

D
Neither of the statements is correct.

Solution

Statement-1:

As shown in the figure,

Statement-2:
Question 20
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In the figure (not drawn to scale), DE ∥ FG ∥ HI, FG ∥ JK, IE ∥ ON, and IE, OM and ON are transversals. Find the values of angles x and y.

A
∠x = 113^o, ∠y = 59^o

B
∠x = 59^o, ∠y = 113^o

C
∠x = 67^o, ∠y = 121^o

D
∠x = 103^o, ∠y = 159^o

Solution

DE ∥ HI and IE is a transversal. (Given)
∠DEI + ∠HIE = 180^o (Co-interior angles)
67^o + ∠x = 180^o
∠x = 113^o

FG ∥ JK and ON is a transversal. (Given)
∠GNO + ∠KON = 180^o (Co-interior angles)
∠121° + ∠y = 180^o
∠y = 180^o- 121^o
∠y = 59^o
Question 21
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Fill in the blanks:

(i) A _______ has one end point and infinity extends in one direction.
(ii) A line segment has _______ end points with a definite length.
(iii) A _________ extends forever in the both directions.
(iv) When a line intersects two or more other lines, it is called ____________.

A
(i) ray (ii) one (iii) line (iv) transversal

B
(i) line segment (ii) two (iii) line (iv) transversal

C
(i) ray (ii) two (iii) line (iv) transversal

D
(i) ray (ii) two (iii) line (iv) parallel

Solution

1. A ray extends indefinitely in one direction, but ends at a single point in the other direction. That point is called the endpoint of the ray.
2. A line segment has two endpoints. A line has no endpoint. A line segment has a definite length.
3. A line extends indefinitely in a single dimension.
4. A transversal is a line that passes through two or more lines in the same plane at two distinct points.
Question 22
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If EP // HO and EH // PO, find the value of x - 2y + z.

A
40^o

B
60^o

C
70^o

D
110^o

Solution

y = 40^o (Alternate interior angle)
∠P = 70^o(Alternate interior angle)
∠P = ∠ H = 70^o (Opposite angles of a parallelogram)
Z = ∠H - 40^o= 70^o - 40^o = 30^o
∠ H + x = 180^o
70^o + x = 180^o
x = 180^o - 70^o = 110^o
x - 2y + z = 110^o - 2(40^o ) + 30^o = 110^o- 80^o + 30^o
= 60^o
Question 23
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Which of the following options holds?

Statement 1: ∠2 and ∠3 are alternate angles.
Statement 2: ∠1 + ∠3 = 180^o

A
Both statement 1 and statement 2 are true.

B
Statement 1 is true and statement 2 is false.

C
Statement 1 is false and statement 2 is true.

D
Both statement 1 and statement 2 are false.

Solution

Statement 1:
∠2 and ∠3 are vertically opposite angles.
Statement 2:
∠1 + ∠3 = 180^o (because they are supplementary angles)
Question 24
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In the given figure (not drawn to scale), DMC is parallel to BLA. EBD, FLMG and HACI are straight and parallel lines.

Find the respective values of the following:
(1) ∠GMC - ∠MCL
(2) ∠FLB + ∠MDB

A
56^o, 180^o

B
180^o, 56^o

C
146^o, 102^o

D
102^o, 146^o

Solution

(1) IH is parallel to GF and CM is a transversal.
Therefore, ∠GMC = ∠MCH
∠GMC = ∠MCL+ 56^o
∠GMC - ∠MCL= 56^o

(2) GF is parallel to DE and LB is a transversal.
∠FLB + ∠EBL= 180^o
∠FLB = 138^o
LB parallel to MD and BD is a transversal.
∠LBE =∠MDB (Corresponding angles)
∠MDB = 42^o
Now, ∠MDB + ∠FLB = 42^o +138^o = 180^o

Question 25

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Mahi got an assignment to name some of the angles formed between a rod and a railway track. The rod is placed on the top of the track lines, as shown below.

Following are some observations made by him. Which of the following is/are correct?

Angles	Observations
(1) Vertical opposite angles	(i) ∠1 = ∠2, ∠7 = ∠3
(2) Supplementary angles	(ii) ∠1 + ∠4, ∠3 + ∠2
(3) Corresponding angles	(iii) ∠4 = ∠7, ∠2 =∠5
(4) Alternate angles	(iv) ∠3 = ∠5, ∠6 = 1

Only (2) and (3)

Only (1) and (4)

Only (1), (2) and (3)

Only (4)

Solution

(1) Vertical Opposite Angles: When two lines intersect, they form two pairs of opposite angles.
In the following figure, vertical opposite angles are:
∠1 = ∠2, ∠3 = ∠4, ∠8 = ∠7, ∠6 = ∠5

(2) Supplementary Angles: Two angles are said to be supplementary when the sum of the two angles is 180°.
In the following figure, supplementary angles are:
∠1 + ∠4, ∠1 + ∠3 , ∠3 + ∠2, ∠2 + ∠4, ∠6 + ∠7, ∠6 + ∠8, ∠8 + ∠5, ∠5 +∠7

(3) Corresponding Angles: the angles which occupy the same relative position at each intersection where a straight line crosses two others.

(4) Alternate Angles: Angles that are on the opposite sides of the transversal are called alternate angles.
In the following figure, alternate angles are ∠1 = ∠5, etc.

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Lines And Angles Test - 6

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Lines And Angles Test - 6

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Question 1

Opposite angels of a parallelogram are congruent.

Each angle of an isosceles triangle is 60o.

The sum of all angles of a square is 180o.

Consecutive angles of a parallelogram are complementary.

Solution

Question 2

∠c =∠f

∠c = ∠e

∠c + ∠b = ∠d

∠a + ∠b = ∠d

Solution

Question 3

EF

CD

AB

GH

Solution

Question 4

60o

75o

70o

80o

Solution

Question 5

44°

31°

49°

51°

Solution

Question 6

120o

140o

155o

125o

Solution

Question 7

25°

28°

30°

32°

Solution

Question 8

125°, 75°

130°, 70°

135°, 65°

140°, 60°

Solution

Question 9

34o

37o

39o

41o

Solution

Question 10

22o

24o

26o

28o

Solution

Question 11

∠AOB + 78o = 180o

∠AOB + ∠COE = 180o

∠BOE + ∠BOC = 180o

∠BOE + ∠OED = 180o

Solution

Question 12

∠j, ∠6

∠4, ∠6

∠4, ∠l

∠m, ∠g

Solution

Each angle of an isosceles triangle is 60^o.

The sum of all angles of a square is 180^o.

60^o

75^o

70^o

80^o

120^o

140^o

155^o

125^o

34^o

37^o

39^o

41^o

22^o

24^o

26^o

28^o

∠AOB + 78^o = 180^o

∠AOB + ∠COE = 180^o

∠BOE + ∠BOC = 180^o

∠BOE + ∠OED = 180^o

68^o

65^o

64^o

60^o

150^o

100^o

90^o

60^o

115^o

116^o

117^o

118^o

36^o

37^o

38^o

39^o

83^o, 69^o, 80^o

69^o, 81^o, 69^o

111⁰,69⁰,69⁰

69⁰,69^o, 83^o

∠x = 113^o, ∠y = 59^o

∠x = 59^o, ∠y = 113^o

∠x = 67^o, ∠y = 121^o

∠x = 103^o, ∠y = 159^o

40^o

60^o

70^o

110^o

56^o, 180^o

180^o, 56^o

146^o, 102^o