Angles Related to Straight Lines and Triangles

11 Angles Related to Straight Lines and Triangles

Summary

Are You Ready? Types of Angles and Naming Angles

1. Write down the size of each of the following marked angles.
(a) (b) (c)

2. The following show the sizes of eight angles.

a = 36 b = 250 c = 145 d = 92
e = 324 f = 190 g = 109 h = 90
Classify the types of the angles by completing the following table.
Type of angle Acute angle Obtuse angle Reflex angle Right angle
Name of angle

3. The figure shows three marked angles. Classify the types of the angles and A
name the angles by completing the following table. C
B
Type of angle Obtuse angle O

Name of angle AOB

Parallel Lines
4. Use the symbol ‘//’ to write down all pair(s) of parallel lines in each of the following figures.
(a) A B (b) Q S (c) B C

C D
P R A D
T
5. Determine whether there are parallel lines in each of the following figures. If yes, mark each pair of
parallel lines with arrowheads.
(a) A D (b) P S (c) P

B C Q R
Q R
ABCD is a parallelogram. PQRS is a trapezium.
PQR is a right-angled triangle.

© Educational Publishing House Ltd 1

Book 1B Chapter 11

11.1 Angles Related to Intersecting Lines

Stage 1
Demonstration 1 Practice 1
In the figure, AOB is a straight line. Find x. (a) In the figure, AOB is a straight line. Find x.
D C
C

x
40 50 B x 100
A A
O
O B

Solution

Tips

[Reference: adj. s on st. line]


a and b are adjacent angles.

Note: (b) In the figure, POQ is a straight line. Find y.

If three or more adjacent angles lie on a straight line, Q
O
the sum of all the adjacent angles is still 180. 42
P 105 y
e.g. S
y R
x z

x + y + z = 180

40 + x + 50 = 180 (adj. s on st. line)

x = 180 – 40 – 50
x = 90

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 Angles Related to Straight Lines and Triangles

Demonstration 2 Practice 2
In the figure, find x. (a) In the figure, find x.
B B
A x

O
112 131 123
O 100
A
C x
C

Solution

Tips

[Reference: s at a pt.]

Note:
If four or more angles are at a point, the sum of all
(b) In the figure, find x.
the angles is still 360.
B
e.g. A
111
x
91 O
88
a + b + c + d = 360 C

x + 131 + 112 = 360 (s at a pt.)

x = 360 – 131 – 112
x = 117

© Educational Publishing House Ltd 3

Book 1B Chapter 11

Demonstration 3 Practice 3
In the figure, the straight lines PQ and RS intersect at O. (a) In the figure, the straight lines PQ and RS intersect
Find x. at O. Find x.
T
P S
P S
106
x
O x 36
T
130 O 45
R Q
R
Q

Solution

Tips

[Reference: vert. opp. s]


a and b are a pair of
vertically opposite angles.

Note:
(b) In the figure, AOB and COD are straight lines.
Refer to the figure below.
Find x.
E D

A B
O
127
There are two pairs of vertically opposite angles:
(1) a and b (2) c and d
C

x + 106 = 130 (vert. opp. s)

x = 130 – 106
x = 24

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 Angles Related to Straight Lines and Triangles

Stage 1 Questions Questions

Generator
In each of the following figures, POQ is a straight line. Find x. (1 – 6)
1. R 2. O Q
P x
147
x
55 R
P Q
O

3. R 4. R
S S

x
34 Q P 37
62 x
O O
P Q

5. 6. P
S
T O
R 94
76 x x
36 Q
30 44 33
P Q T
O
R
S

In each of the following figures, find x. (7 – 12)

7. 8.
224 A
x
O O
A B
x
B 221

9. 10. A
B
A 201
80 O x
O 69
C 86
x B

11. B 12. B
A A
x

C 41
141 O x
82 52 C
D O
185
D

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Book 1B Chapter 11

In each of the following figures, straight lines PQ and RS intersect at O. Find x. (13 – 18)
13. R 14. S

Q
x 132
P Q
O O
58 x
P

S R

15. T
16. S
P
P S
98 30 36 O
T x
O 43
x
Q Q
R R

17. T 18. R
S T
P x
88 x
29
P Q
O O 44
111
Q S
R

19. In the figure, AOB and COD are straight lines. E

D
(a) Find x.
(b) Find DOE. x
A B
40 O

20. Refer to the figure. A

146
(a) Find x. 79
O
D
x
(b) Find BOD.
B C

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 Angles Related to Straight Lines and Triangles

Stage 2
Demonstration 4
In the figure, the straight lines AB and CD intersect at Solution

O. Find x and y. x + 56 = 180 (adj. s on st. line)


C x = 180 – 56 A C
A y
y
x = 124 x
x y = 56 (vert. opp. s) O
O  56
A C B
56 D
y
B x
D O
56
B
D

Demonstration 5
Solution
In the figure, the straight lines AB, CD and EF intersect
at O. Find x. Tips
F F
F A A
A ? ?
x 80 x 80
C D C D
x 80 O O
C D 60 60
O B B
60 E E
B
E
AOF = ? Find AOF first.

AOF = 60 (vert. opp. s)

x + AOF + 80 = 180 (adj. s on st. line)
x + 60 + 80 = 180
x = 180 – 60 – 80
x = 40

Demonstration 6
Refer to the following figure. Solution

A (a) x + x + 30 + 210 = 360 (s at a pt.)

2x + 240 = 360
x 2x = 360 – 240
210 O B
x 2x = 120
30 x = 60
C
D (b) BOD = 60 + 30
(a) Find x. = 90
(b) Is OB perpendicular to OD? Explain your answer. ∴ OB is perpendicular to OD.

© Educational Publishing House Ltd 7

Book 1B Chapter 11

Check Yourself
1 2
In the figure, the straight lines AB and CD intersect at In the figure, the straight lines AB, CD and EF intersect
O. Find x. at O. Find x.
C C E
A
B 36
45
O O
y 105
x x
A
B
D D
F

3 4 (Try more)
Refer to the following figure. In the figure, AOB is a straight line. Find x and y.
A
D
A
240
x + 60 O y
x x y + 40
C
O
B
C 2y – 8
B
(a) Find x.
(b) Is OA perpendicular to OB? Explain your answer.

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 Angles Related to Straight Lines and Triangles

Stage 2 Questions
In each of the following figures, AOB is a straight line. Find x. (1 – 2)
1. O
2. D
A B
2x C
7x

C x
x – 20 x + 5
A B
O

In each of the following figures, find x. (3 – 4)

3. A 4. B
A
109
x 8x x
B 2x + 10 O
O
3x 115 C

C D

In each of the following figures, the straight lines PQ and RS intersect at O. Find x. (5 – 6)
5. 6. S
R

T Q
74 O
2x Q x
O
P 3x
P
90 – x

R
S

7. In the figure, the straight lines AB and CD intersect at O. Find x and y. A D

106

O x

y
C B

8. In the figure, the straight lines PQ and RS intersect at O. Find x and y. P

y
O
R S
x 75

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Book 1B Chapter 11

9. In the figure, AOB is a straight line. Find x and y. B

x
O
C
40
y

A
D

10. In the figure, the straight lines AB, CD and EF intersect at O. Find x. F

D
A 84

x
O 50 B
C
E

11. In the figure, the straight lines AB, CD and EF intersect at O. C

A
If AOE = COF = 49, find BOD.
O F

B
D

12. In the figure, POQ is a straight line. S

(a) Find x.
EYA (b) Is ROS a right angle? Explain your answer. R x + 19
x
21 Q
P
O

13. Refer to the figure.

200
(a) Find x. O
S
x + 25
EYA (b) (i) Is POQ equal to QOR? Explain your answer. P 45
x
(ii) Is OP perpendicular to OR? Explain your answer.
Q R

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 Angles Related to Straight Lines and Triangles

Try More Questions

14. In the figure, the straight lines AB, CD and EF intersect at O. F

Find x and y. A
D
x
O
69
3y

2y – 3 B
C
E

15. In the figure, the straight lines AB, CD and EF intersect at O. F D

A
(a) Find x and y.
x
EYA (b) Is BOD a right angle? Explain your answer. x + 8
O

y
41
B
C E

16. In the figure, POQ and ROS are straight lines. Find x and y. P

y x – 15
R S
O x + 15

EYA 17. In the figure, the straight lines AB, CD and EF intersect at O. D

AOC = x, BOF = y and DOE = x + y. Someone claims

E
that CD must be perpendicular to EF. Do you agree? Explain
O
A B
your answer.
F

EYA 18. In the figure, AOB is a straight line and AOE = COD = 90. C

Someone claims that BOC must be equal to DOE. Do you

agree? Explain your answer.
B
O

A D

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Book 1B Chapter 11

Multiple Choice Questions

19. In the figure, AOC is a straight line. Which of the 22. In the figure, AOB is a straight line.
following statements must be true? If AOC = BOD = 55, find COD.
B D
A C
p

s O q
r
C
A B
D O
I. p + q = 180 A. 55
II. p=r B. 60
III. p + q + r + s = 360 C. 65
A. I and II only D. 70
B. I and III only
C. II and III only 23. In the figure, AOB and COD are straight lines.
D. I, II and III If AOC = 118 and BOD = 2DOE, find
BOE.
20. In the figure, AOB is a straight line. Find x. A

B D
O
O
A x 107
36 C E

C B
D A. 31
A. 28 B. 54
B. 37 C. 59
C. 47 D. 62
D. 54
24. In the figure, AOB, COD and EOF are straight
21. In the figure, find x. lines. Find BOE.
B F

A
125
D
105 72 C 28
O O
C
A B
x
E

A. 203 A. 27
B. 193 B. 29
C. 183 C. 32
D. 173 D. 37

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 Angles Related to Straight Lines and Triangles

11.2 Angles Related to Parallel Lines

Stage 1

Demonstration 1 Practice 1

In the figure, AB // CD. Find x, y and z. (a) In the figure, PQ // RS. Find a.

x
A B P Q
y z 75
50 a
C D R S

Solution

Tips

[Reference: corr. s, AB // CD]

(b) In the figure, PQ // RS. Find b.

P Q
b
62
[Reference: alt. s, AB // CD] R S

[Reference: int. s, AB // CD]

(c) In the figure, PQ // RS. Find c.

P Q
c
R S
80

x
x = 50 (corr. s, AB // CD)  A y
B
z
y = 50 (alt. s, AB // CD) C
50
D

z + 50 = 180
z = 130 (int. s, AB // CD)

© Educational Publishing House Ltd 13

Book 1B Chapter 11

Demonstration 2 Practice 2
In the figure, AB // CD. CED is a straight line. Find x (a) In the figure, AB // CD. Find x.
and y. 30
40
A B A B
55
x x
C D

72 y
C D
E

Solution

(x + 55) + 72 = 180 (int. s, AB // CD)

x + 127 = 180 
A (b) In the figure, AB // CD. AEB is a straight line.
B
x = 53 x
55 Find x and y.
E
A B
x y
72 y
C D
E
68
43
C D
y = 55 (alt. s, AB // CD)

A B
55
x

72 y
C D
E

(c) In the figure, AB // CD. AEB is a straight line.

Find x and y.
B D

E
y
66
77 x
A C

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 Angles Related to Straight Lines and Triangles

Stage 1 Questions Questions

Generator
In each of the following figures, AB // CD. Find x. (1 – 4)
1. 2.
54
A B A B
x
x
C D 71
C D

3. 4.
A B
A B
x
126 143
x C D
C D

In each of the following figures, AB // CD. Find x and y. (5 – 8)

5. 6. x
y
A B A B
x y

65 122
C D C D

7. B D 8. B D

x x
63 y
y
134

A C A C

In each of the following figures, AB // CD. Find x, y and z. (9 – 10)

9. 10.
z B B
A x y
76 A
118 D D y z
C x C

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Book 1B Chapter 11

In each of the following figures, PQ // RS. Find x. (11 – 14)

11. 12.
x
42
P Q P
x
86
35 Q
R S R 75
S

13. Q 14. Q
S

P 134 S
x 75

50
R x 82
P
R

In each of the following figures, PQ // RS. Find x and y. (15 – 16)

15. 16. P
x
65
P Q
y x
R y
50 Q
39
60
R S
S

In each of the following figures, PQ // RS. Find the unknowns. (17 – 20)
17. 18. P Q
Q 82
116
P x 77
T

66 S
n
R y
m n
R S
PTR is a straight line.

19. Q 20.
S
T
P Q
y 85 y
x x
47 35
x
P R S
U

3x PTQ and RUS are straight lines.

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 Angles Related to Straight Lines and Triangles

Stage 2
Demonstration 3

In the figure, AB // CD. AEB and CFD are straight lines.

E x
A B
Find x.
125
C D
F

Solution
Tips Method 1

x x
125 + EFD = 180 (adj. s on st. line)
E E
A B A B
EFD = 180 – 125
125 125
C
?
D C
?
D
EFD = 55
F F
x = EFD (corr. s, AB // CD)
EFD = ? Find EFD first. = 55

Method 2 Method 3
AEF + 125 = 180 (int. s, AB // CD) BEF = 125 (alt. s, AB // CD)
AEF = 180 – 125 x + BEF = 180 (adj. s on st. line)
AEF = 55 x + 125 = 180
x = AEF (vert. opp. s) x = 180 – 125
= 55 x = 55

Demonstration 4
B
In the figure, AB // CD // EF. BDF = 60 and EFD = 153. A
x
Find x. C D
60
153
E
F
Solution
Tips CDF + 153 = 180 (int. s, CD // EF)
A B
Find CDF (i.e. z). CDF = 27
x
y BDC = 60 – 27 ◄ BDC + CDF = BDF
C D
z 60 Find BDC (i.e. y). = 33
153
E x + BDC = 180 (int. s, AB // CD)
F
Find x. x + 33 = 180
x = 147

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Book 1B Chapter 11

Check Yourself
1 2
In the figure, AB // CD. AEB and CFD are straight lines. In the figure, RPQ = 118 and RTU = 123.
Find x. If PQ // RS // TU, find PRT.
A P Q
E
42
B
C F S
R
x
D
U
T

3 4 (Try more)
In the figure, AB // DE // FC. Find x. In the figure, AB // DE.
C E
F B
D
54 111
108
x A x
D E
133 C
A B
(a) Draw a straight line CF such that CF // AB // DE.
(b) Find x.

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 Angles Related to Straight Lines and Triangles

Stage 2 Questions
In each of the following figures, AB // CD. AB and CD intersect EH at F and G respectively. Find x. (1 – 4)
1. E 2. E
67
A B A F
F
x B
G C
C D G
x
D
73
H
H

3. E 4. A C
x B
F
A E
F
111 D
109 G
G
C x H

H B D

In each of the following figures, PQ // RS. Find the unknowns. (5 – 6)

5. x 6.
S Q
Q
S
63
y m
R
112 T 81 n
P P T
U R
PRT is a straight line.
STU is a straight line.

In each of the following figures, AB // CD // EF. Find x and y. (7 – 8)

7. 8.
F B
y
E A x
D x 135
D
C C
B 127 y F

A E

In each of the following figures, AB // CD and EF // GH. AB intersects EF and GH at P and Q respectively. CD
intersects EF and GH at S and R respectively. Find x and y. (9 – 10)
9. F H 10. F H
P 55 Q x
A B A P
x Q B
118
y y
S S R
C D C D
R

E G E G

© Educational Publishing House Ltd 19

Book 1B Chapter 11

In each of the following figures, AB // CD // EF. Find x. (11 – 12)

11. A B 12. A B
x
99

107 D C D
C
125
x
64
E F
E F

Try More Questions

In each of the following figures, AB // CD. Find x. (13 – 16)
13. A B 14. A B
x 28
231
E x
E

C D 45
C D

15. E 16. A
B
27
115
C
75 100 D
A B E
x
C D x

17. In the figure, AB // EF. ABC = 50, reflex BCD = 230 and A B

DFE = 110. Find CDF.

C

E F

18. In the figure, AD // CE. a and c are acute angles and b is an A C

obtuse angle. Show that b = a + c. a b c

D E

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 Angles Related to Straight Lines and Triangles

19. In the figure, PUR and RVS are straight lines and PQ // RS. P
Q
x and y are obtuse angles. Express y in terms of x such that x

△RUV is a right-angled triangle. U

y
R S
V

Multiple Choice Questions

20. Refer to the figure. Which of the following 22. In the figure, PQ // RS. QPR = QRS and
statements must be true? PRQ = 60. Find QRS.

P Q
p
A B
q
A. 45
s r B. 50
C D C. 60
S
D. 80 R
I. p and r are a pair of corresponding angles.
II. p and s are a pair of alternate angles. 23. In the figure, find x.
III. q and r are a pair of interior angles on the x
same side.
70
A. I and II only
B. I and III only
C. II and III only
A. 290
D. I, II and III
B. 270
C. 235
21. In the figure, AB // CD. Find x.
D. 210
B D

2x – 17 x + 5
24. In the figure, BAD = 30 and ADE = 130.
If DE // BC, find ABC.
A. 22
A
B. 34
A C
C. 43
D. 64 D
A. 160 E

B. 150
C. 130 C
B
D. 100

© Educational Publishing House Ltd 21

Book 1B Chapter 11

11.3 Angle Sum of a Triangle

Stage 1
Demonstration 1 Practice 1
In each of the following figures, find x. (a) In the figure, find x. B

(a) B
63
A 59
95
x x
30
A C
C

(b) P

60

x x
Q R

Solution (b) In the figure, find x. P Q

33
Tips
x
[Reference:  sum of △]
R


a, b and c are interior angles of △ABC.

(c) In the figure, find x. D

(a) In △ABC, x
30 + 95 + x = 180 ( sum of △) 108 x F
x = 180 – 30 – 95 E
x = 55

(b) In △PQR,
60 + x + x = 180 ( sum of △)
2x = 180 – 60
2x = 120
x = 60

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 Angles Related to Straight Lines and Triangles

Demonstration 2 Practice 2
In the figure, ADC and BEC are straight lines. Find x (a) In the figure, PSQ is a straight line. Find x.
and y. P
A
x
75 S
D 60
105 30 40
70 y Q R
x
B C
E

Solution

75
D

105
70 y x
B C
E

(b) In the figure, ADB and BEC are straight lines.

In △ABC, Find x and y.
75 + 70 + x = 180 ( sum of △) A

x = 180 – 75 – 70 D

85
x = 35 y

x 80 60
B C
E
A

75
D
35
105
70 y x
B C
E

In △CDE,
x + 105 + y = 180 ( sum of △)
35 + 105 + y = 180
y = 180 – 35 – 105
y = 40

© Educational Publishing House Ltd 23

Book 1B Chapter 11

Stage 1 Questions
In each of the following figures, find x. (1 – 6)
1. A 2. C
48
50
A 36
x
x C
62 B

3. A 4. A
x
x C
61
102 39
C B
B

5. A 6. A

78 x

x x
B C x
B C

In each of the following figures, find x. (7 – 8)

7. P 8. P

38 52 45

x
44 x 45 34
Q R Q R

9. In the figure, ADC is a straight line. Find ABD. A

D
C
62 33

50

10. In the figure, BDC is a straight line. ABD = 70, A

BAD = 46 and ACD = 36.

(a) Find CAD.
(b) Find ADC.
B C
D

24 © Educational Publishing House Ltd

 Angles Related to Straight Lines and Triangles

11. In the figure, QRST is a straight line. PQR = QPR = 32 P

and PTS = SPT = 28. Find RPS.

Q T
R S

In each of the following figures, ADC and BEC are straight lines. Find x and y. (12 – 13)
12. A 13. A
50
85 D
x B
y
E
D 67 23
40 46 x y
B C
E C

14. In the figure, AC and BD intersect at E. A

D
(a) Find CBD. 65
(b) Find ACD. E 60

30
44
B C

15. In the figure, PSR and QST are straight lines. PTQ = 56, P T
QPR = 38, TPR = 32 and TQR = 55. Find PQT
and PRQ. S

Q R

16. In the figure, AGC, DGE and BECF are straight lines. A
D
ABC = 65, BAC = 54, EDF = 53 and DFE = 62.
G
Find EGC.

B F
E C

© Educational Publishing House Ltd 25

Book 1B Chapter 11

Stage 2
Demonstration 3
A
In the figure, AE and BD intersect at C. Find x.
D
x
C 47

38 43

B E
Solution
Tips In △CDE,
A A
DCE + 47 + 43 = 180 ( sum of △)
D D
x x DCE = 180 – 47 – 43
C 47 C 47
?
? DCE = 90
38 43 38 43
ACB = DCE = 90 (vert. opp. s)
B E B E In △ABC,
ACB = ? Find DCE first.
x + 90 + 38 = 180 ( sum of △)
x = 180 – 90 – 38
x = 52

Demonstration 4

In the figure, BEC is a straight line. If AB // CD, Solution

find x. ABE = 62 (alt. s, AB // CD)
A B In △ABE,
40
40 + 62 + x = 180 ( sum of △)
x
x = 180 – 40 – 62
E x = 78
62
C D

Demonstration 5
In the figure, ADB and AEC are straight lines. Solution

If DE // BC, find x. AED = 77 (corr. s, DE // BC)

A In △ADE,
54 54 + 77 + x = 180 ( sum of △)
D x x = 180 – 54 – 77
E x = 49
B
77

26 © Educational Publishing House Ltd

 Angles Related to Straight Lines and Triangles

Check Yourself
1 2
In the figure, PT and QS intersect at R. Find x. In the figure, BEC is a straight line. If AB // CD, find x.
P Q B
34 45

R
D
x 64
42 x A
S T E
57

3 4 (Try more)
In the figure, ADB and BEC are straight lines. In the figure, AD and BC intersect at E. If AB // CD,
If AC // DE, find x. find x.
A D
B
x
55
D E
126

x 74
B C 38 42
E A C

© Educational Publishing House Ltd 27

Book 1B Chapter 11

Stage 2 Questions
In each of the following figures, find x and y. (1 – 4)
1. A 2. 314
A
72
x
y
40 x
B D
C 88 y
BCD is a straight line. B C

3. A B 4. A
C
x
117 x C
x 126

x y
y
B
D
ABC is a straight line.

5. In the figure, AFGB, CFD and CGE are straight lines. C

Find x. x

A F
x
G B
46
D
E

6. In the figure, AE and BD intersect at C. Find x. E

32
D
56

52
x B
A

7. In the figure, ACF and BCDE are straight lines. Find x. A

E
D
50
3x
C

x
310 B
F

28 © Educational Publishing House Ltd

 Angles Related to Straight Lines and Triangles

In each of the following figures, AB // CD. Find x. (8 – 17)

8. D 9.
A B
58

x 75
E C D
B C
38 x

E
A
BEC is a straight line. ADE is a straight line.

10. B 11. A C

29
D
x
A 93
C 26 x
44
E B D
E

ACE and BDE are straight lines. EBD is a straight line.

12. A B 13. B D
x
E x
28
114
56
25 A C
C D E

AEC is a straight line. AEC is a straight line.

14. A 15. B
A
C 71
69 62 x
60 E
x

B E
29
C D

16. B 17. B

A 215
A x

D
54 D
88
36 36 62 x
C E E
C
ADE is a straight line.

© Educational Publishing House Ltd 29

Book 1B Chapter 11

Try More Questions

18. In the figure, AB // CD. E is a point on BD such that C

ECD = CED = 28. Find ABD. A

E
B

19. In the figure, ABCD is a trapezium, where AD // BC. A D

ABC = 130, ACD = 85 and BAC = CAD.

Find ADC.

B C

20. In the figure, AB // CE. D is a point on CE such that A B

CBD = CDB. BDE = 115 and ABC = ACB.

Find BAC.

C D E

21. In the figure, PS and QR intersect at T. PSQ = 46, P Q

QPS = 38 and QRS = 43. If PQ // RS, find RQS.

R
S

22. In the figure, AB // EC and BE // CD. AC and BE B

C
intersect at F. BAC = 56 and CBE = 44. x x + 4
(a) Find x.
(b) Find DCE. F

A D

30 © Educational Publishing House Ltd

 Angles Related to Straight Lines and Triangles

EYA 23. In the figure, PR and QS intersect at T. QPR = QSR = a and P S

PRQ = SQR = b, where a and b are acute angles. Someone
claims that PQS must be equal to PRS. Do you agree? T
Explain your answer.

Q R

Multiple Choice Questions

24. In the figure, find x. 26. In the figure, PTR is a straight line. If PQ // RS,
find TQR.
300 A
Q S

x x
B C 63
56 80
P T R
A. 40
B. 45 A. 17
C. 50 B. 19
D. 60 C. 24
D. 28
25. In the figure, AEB, BFG and CEFD are straight
lines. Find x. 27. In the figure, AED is a straight line and AB // CD.
G D ACD = 69, CAD = 63 and ABE = BAE.
46
Find AEB.
F
A B

128 x
A B
E
C C D

A. 52
A. 66
B. 64
B. 78
C. 82
C. 84
D. 96
D. 96

© Educational Publishing House Ltd 31

Book 1B Chapter 11

Appendix

Figure Condition Result Reference

○,1

AOB is a straight line. a + b = 180° adj. s on st. line

○,2

a, b and c are
a + b + c = 360° s at a pt.
angles at a point.

○,3
AOB and COD are
a=b vert. opp. s
straight lines.

○,4

a=b corr. s, AB // CD

○,5

AB // CD a=b alt. s, AB // CD

○,6

a + b = 180° int. s, AB // CD

○,7

ABC is a triangle. a + b + c = 180°  sum of △

34 © Educational Publishing House Ltd