1916LCOL3Bk2SolutionsChapter5resources-1916 LC OL 3 Bk 2-1916_LCOL3_Bk2_Solutions_Ch05

8/17/2019 1916LCOL3Bk2SolutionsChapter5resources-1916 LC OL 3 Bk 2-1916_LCOL3_Bk2_Solutions_Ch05

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Active Maths 3 Book 2 – Strands 1–5 – Ch 5 Solutions 1

Chapter 5 Exercise 5.1

Q. 1. (iv) RP FE

(v) XZ ZY

(vi) A, C, Y , B

(vii) X

Q. 3. (i) 70° acute

(ii) 115° obtuse

(iii) 45° acute

(iv) 260° reflexive

(v) 120° obtuse

Q. 5. (iv) No

Q. 6. (i) 180° − 115° = 65°

(ii) 180°−

63°−

90° = 27°

(iii) 90° − 46° = 44°

(iv) 180° − 53° = 127°

127° ÷ 2° = 63.5°

(v) 360° − 150° − 90° = 120°

(vi) 360° − 25° = 335°

(vii) 180° − 15° − 63° − 37° = 65°

Q. 7. (i) 6 x + 3 x = 90°

9 x = 90°

x = 10°

(ii) 5 x + 6 x + 40° + 100° = 360°

11 x = 360° − 140°

11 x = 220°

x = 20°

(iii) 5 x + 10° + 93° + 7 x + 5° = 180°

12 x = 180°−

108°12 x = 72°

x = 6°

(iv) 7 x + 5 + 25 + 8 x − 30 = 180°

7 x + 8 x = 180°

15 x = 180°

x = 12°

Q. 8. (i) 4 x° = 90°

x = 22.5°

6 x° + y = 180°

6(22.5)° + y = 180°

y = 45°

(ii) 2 x + 30° + 8 x = 180°

10 x = 150°

x = 15°

62° + 8 y + 54° = 180°

8 y = 180° − 116°

8 y = 64°

y = 8°

Exercise 5.2

Q. 1. (i) 65° Vertically opposite

(ii) 55° Vertically opposite

(iii) 63° Vertically opposite

(iv) 90° Vertically opposite

Q. 2. (i) B = 25° C = 155°(ii) B = 100° C = 100°

(iii) 2B = 70°

B = 35°

C = 110°

(iv) B = 90°

3C = 90°

C = 30°

Q. 3. (i) x + 20 = 60

x = 40

35° + 60+ y + 30 = 180

125 + y ° = 180°

y = 55°


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2 Active Maths 3 Book 2 – Strands 1–5 – Ch 5 Solutions

(ii) x + y + 70 + 80 = 180 Straight line x + y = 30

1 __ 2

x + 7 __ 4

y = x + y Vertically opposite

1 __ 2

x –3

__ 4

y = 0

x + y = 30

1 __ 2

x –3

__ 4

y = 0 (× 2)

x + y = 30

( x – 1.5 y = 0)

2.5 y = 30

y = 12°

x + 12 = 30

x = 18°

Exercise 5.3

Q. 1. (i) ∠1 = 145° Corresponding

∠2 = 180° − 145°= 35° Straight line

(ii) ∠1 = 148°

∠2 = 148° Vertically opposite

(iii) ∠1 = 73° Corresponding

∠2 = 107° Straight line

(iv) ∠1 = 84° Alternate


(v) ∠1 = 72° Alternate


Q. 2. (i) Yes

(ii) Yes

(iii) No

Q. 3. (i) D = 150° Straight line

A = 150° Alternate

B = 30° Straight line

C = 210° (360° − 150°)

(ii) A = 84° Vertically opposite

B = 84° Corresponding

C = 96° Straight line

D = 96° Vertically opposite

(iii) ∠1 = 180° − 15° − 137° = 28°

∠3 = 180° − 28° = 152°

∠2 = 137° Corresponding

∠4 = 360°−

43°−

137°−

152°= 28°

(iv) C = 99° Straight line

D = 99° Corresponding

B = 81° Straight line

A = 99° Alternate

(v) D = 75° Straight line

A = 75° Corresponding

B = 75° Opposite angles

C = 105° Opposite angles

(vi) ∠1 = 104° Straight line

∠2 = 117° Corresponding

∠4 = 117° Vertically opposite

∠3 = 63°


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Q. 4. (i) 4 x – 30 + x = 180°

5 x = 180 + 30 = 210°

x = 42°

y = 180° – x

= 180° – 42°

y = 138°

(ii) Eqn 1: x + y + 47 + x + y – 39 = 180 Straight line 2 x + 2 y = 172

x + y = 86

Eqn 2: 2 x + 3 y – 87 = 72 + x + y – 39 Alternate

x + 2 y = 120

x + y = 86

– ( x + 2 y = 120)

–y = –34

y = 34°

∴ x + 34 = 86

x = 52°

Exercise 5.4

Q. 1. (i) A = 90°

B = 180° − 90° − 37° = 53°

(ii) B = 60°

A = 120°

(iii) A = 75°

B = 180° − 150° = 30°

(iv) A = 70° − 50° = 20°

B = 180° − 20° − 110° = 50°

(v) B = 40°

A = 180° − 50° − 40° = 90°

Q. 2. (i) 180° − 96° = 84°

84° ÷ 2° = 42°

X = 42°

Y = 42°

Z = 180°− 84°− 42° = 54°

X = 42°

Y = 42° Z = 54°

(ii) X = 49°

Z = 73°

Y = 180° − 49° − 73° = 58°

(iii) X = 60°

Y = 48°

Z = 180° − 48° − 48° = 84°

(iv) Y = 32°

X = 180° − 120° − 32° = 28°

Z = 28°

(v) Y = 120°

Z = 60°

X = 60° + 85° = 145°

(vi) Z = 180° − 61° − 43° = 76°

Y = 180° − 76° = 104°

X = 180° − 61° − 104° = 15°

(vii) Y = 61°

W = 119°

Z = 180° − 61° − 45° = 74°

X = 360° − 119° − 40° − 135°= 66°


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Q. 3. (i) B = 2 A + A

B = 3 A

3

__ 2

A + B = 180°

3

__ 2

A + 3 A = 180°

3 A + 6 A

________

2

= 180°

9 A = 360°

A = 40°

B = 120°

Q. 4. (i) Eqn 1: 6 x + y + 9 + 4 x + 3 y – 9 = 180 Straight line

10 x + 4y = 180

5 x + 2y = 90

Eqn 2: 6 x + y + 9 = 46 + 2 x + 3 y – 19 Exterior Angle

2 x – 2y = 18

5 x + 2y = 90

+ (4 x – 2y = 18)

9 x = 108

x = 12

5(12) + 2y = 90

2y = 30

y = 15

(ii) 3 x + y + 9 y + x – 3 + 6 x + 3 y – 4 = 180

10 x + 13 y = 187

6 x + 3 y – 4 + 12 x – 5 y – 14° = 180

18 x + 8 y = 198

10 x + 13 y = 187 × 8

18 x + 8 y = 198 × 13

80 x + 104 y = 1496234 x + 104 y = 2574

–154 x = –1078

x = 7

10(7) + 13 y = 187

13 y = 117

y = 9

(ii) B = 180° − 68° = 112°

A = 68° ÷ 2° = 34°

6 x + 3y – 4


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Exercise 5.5

Q. 1. (i) ∠ A

(ii) ∠1

(iii) ∠ XZY

(iv) ∠ ACB

(v) ∠2

Q. 2. Longest Shortest

(i) c b

(ii) [BC ] [ AB]

(iii) [DE ] [DF ]

(iv) [PQ] [QR ]

(v) [RT ] [ST ]

Q. 3. (i) No

(ii) Yes

(iii) Yes

(iv) Yes

(v) No

(vi) No

(vii) Yes

(viii) No

(i x) Yes

(x) No

Q. 4. Yes

Q. 5. (i) Min

n > 7.2 − 6.1

n > 1.1

n = 2

(ii) Largest

n < 6.1 + 7.2

n < 13.3

n = 13

Q. 6. (i) Min n > 11.7 − 6.4

n > 5.3

n = 6

(ii) Max n < 6.4 + 11.7

n < 18.1

n = 18

Q. 7. 8 + 10 = 18 ∴L = 17.99 m

10 – 8 = 2 ∴S = 2.01 m

(i) Largest value = 17.99 m

Smallest value = 2.01 m

(ii) Min 8 + 10 + 2.01

= 20.01 × ¤5

= ¤100.05

Max 8 + 10 + 17.99= 35.99 × ¤5

= ¤179.95

Q. 8. A: 4, 6, 2 4 + 2 = 6 ∴ not atriangle

B: 3, 5, 4 3 + 5 > 4

5 + 4 > 3

4 + 3 > 5 ∴ triangle

C: 8, 7, 7 not a scalene triangle

D: 4, 5, 6 4 + 5 > 6

5 + 6 > 4

6 + 4 > 4 ∴ triangle

Answer: B and D

Q. 9. 4 different parts

A: 50, 60, 1 ü C: 50, 1, 1.5 û

B: 50, 60, 1.5 û D: 60, 1, 1.5 ü

2 (50 cm, 60 cm, 1 m)

or

(60 cm, 1 m, 1.5 m)


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Q. 10. Sheena

3 x + 1 + 5 x – 4 + 7 = 12

8 x – 4 = 12

x = 1

x = 1 then sides are

4, 1, 7

4 + 1 < 7 ∴ not triangle

Elle

8 x + 4 = 16

x = 1.5

x = 1.5 then sides are

5.5, 3.5, 7

5.5, 3.5, 7 form triangle

Elle, Sheena’s sides do not form a

triangle.

Q. 11. (i) b > 14 − 9

b > 5

b = 6

(ii) b < 9 + 14

b < 23

b = 22

(iii) 6 b 22

Q. 12. (i) c > 16 − 10

c > 6

c = 7

(ii) c < 10 + 16

c < 26

c = 25

(iii) 7 c 25

Exercise 5.6

Q. 1. (i) A = 85°

B = 95°

C = 95°

(ii) A = 180° − 77° = 103°

C = 103°

B = 77°

(iii) A = 42°

B = 77°

C = 61°

(iv) A = 78°

B = 180° − 28° − 78° = 74°

C = 102°

(v) A = 32°

B = 62°

C = 180° − 40° − 62° = 78°

Q. 2. (i) |∠BAD| = 60°

(ii) | AB| = 8(iii) |∠ ADC| = 120°

Q. 3. (i) 16

(ii) 18

(iii) 16

(iv) 5.8

Q. 4. (i) A = 180° − 74° = 106°

C = 106° − 32° = 74°

B = 74°

(ii) A = 14°

C = 83°

B = 14°

(iii) A = 180° − 36° − 80° = 64°

C = 64°

B = 36°

(iv) A = 90°B = 180° − 90° − 27° = 63°

C = 27°

D = 27°


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Q. 5. (i) 3 x + 10 = 4 x – 5 (Corresponding angles)15 = x

3 x + 10° = y 3(15) + 10 = y

55° = y

(ii) 5 x + 2 y + 40 + 100 = 180

5 x + 2 y = 40

3 x + 6 y + 8 + 10 x + 11 y + 9 = 180

13 x + 17 y = 163

5 x + 2 y = 40 × 13

13 x + 17 y = 163 × 5

65 x + 26 y = 520

–(65x + 85y = 815)

– 59 y = –295 y = 5

5 x + 2(5) = 40

5 x + 10 = 40

5 x = 30

x = 6

Q. 6. (i) Eqn 1: x + y – 3 + 4 x + y + 3 + 2 x + 5 y –23 = 180 (Triangle)

7 x + 7 y = 203

x + y = 29

Eqn 2: 3 x + 4 y + 9 + 4 x – y + 6 + x + y – 3 = 180 (Interior Triangle)

8 x + 4y = 168

2 x + y = 42

x + y = 29

– (2 x + y = 42)

– x = –13

x = 13

13 x + y = 29

y = 16

Yes, |


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Revision Exercises

Q. 1. (a) (i) ∠ ABC

(ii) ∠CBD

(iii) ∠EBD

(iv) ∠EBD

(v) [BE

(vi) BD

(vii) ∠ ABE, ∠EBD

(b) (i) F

(ii) T

(iii) T

(iv) T

(v) TQ. 2. (a) (i) 85° (v) 85°

(ii) 110° (vi) 95°

(iii) 95° (vii) 95°

(iv) 70° (viii) 110°

(b) Opinion of students

Q. 3. (a) (ii) Corresponding angles

(iii) Vertically opposite angles

(iv) Supplementary angles

(v) Alternate angles

(vi) Corresponding angles

(b) (i) No

(ii) Yes

(c) (i) Yes

(ii) No

Q. 4. (a) (i) A = 43°

B = 180°− 43°− 81° = 56°

C = (180°− 124°) ÷ 2° = 28°

(ii) A = 180° − 122° = 58°

C = 58°

D = 32°

B = 180° − 32° = 148°

(iii) B = 150°

C = 30°

A = 92°

D = 60°

(iv) C = 87°

B = 180° − 87° − 26° = 67°

A = 67°

D = 113°

(v) A = 180° − 90° − 84° = 6°

B = 180° − 126° − (123° − 84°)

= 15°

C = 180° − 90° − 15° = 75°

(b) (i) No

(ii) No

(iii) Yes

(iv) Yes

(v) No

Q. 5. (a) (i) A = 100°

B = 100°

C = 80°

(ii) A = 90°C = 32°

B = 180°− 90°− 32° = 58°

(iii) A = 75°

B = 75° − 20° = 55°

C = 180° − 50°− 75° = 55°

(iv) A = 180° − 56°− 85° = 39°

B = 42°

C = 180°−

42°−

78° = 60°

(b) (i) F

(ii) F

(iii) T

(iv) T

(v) F

(c) Two properties


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Q. 6. (a) (i) 2 x + 6 y + 130° = 180°

4 x + 2 y + 130° = 180°

− 2 x + 6 y = −

50°

12 x + 6 y = 150°

10 x = 100°

x = 10°

2(10) + 6 y = 50°

6 y = 30°

y = 5 °

(ii) 9 x − y = 114°

3 x + 2 y = 66°

18 x – 2 y = 228°

3 x – 2 y = 66°21 x = 294°

x = 14°

9(14) − y = 114°

y = 126° − 114°

y = 12°

(iii) 8 x + 14 y = 98°

16 x − 10 y = 82°

16 x + 28 y = 196°

− 16 x ⊕ 10 y = − 82°

38 y = 114°

y = 3°

8( x) + 14(3) = 98°

8 x = 56°

x = 7°

−

(b) (i) 180 − x2 − 8 x + 5 − 2 x2 −4 x − 10 = x2 + 3 x

−

3 x2 −

12 x + 175 = x2 + 3 x 4 x2 + 15 x − 175 = 0

(4 x + 35)( x − 5)

x = –35

___

4 x = 5

(ii) ∠ A 52 + 8(5) − 5 = 60°

∠B 2(5)2 + 4(5) + 10 = 80°

∠C 52 + 3(5) = 40°

Q. 7. (a) (i) [ AB]

[BC]

[ AC]

(ii) [EF ]

[DF ]

[DE]

(iii) [QR]

[PQ]

[PR]

(b) Name parallelograms

(c) (ii) B, C


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Q. 8. (a) (i) Always (v) Never

(ii) Sometimes (vi) Always

(iii) Sometimes (vii) Always

(iv) Sometimes

(b) (i) 5(2) + 8(2) = 26 km

(ii) 5 x − 3 y = 8

2 x − y = 5

5 x –3 y = 8

− 6 x ⊕ 3 y = − 15 5(7) − 3 y = 8

− x = −7 −3 y = −27

x = 7 y = 9

| AC| = 2(4(7) –5

__ 2

(9))

= 11

11 + 5 + 8 = 24 km

(c) (i) 100 + 75 = 175 km longest (ii) 25 km 25 − 16 n < 25 + 16

n > 9 n < 41

n = 10 mm n = 40 mm

= 1 cm = 4 cm

Cost = $25 Cost = 4 × 25 = $100

$1.25 = €1 $1.25 = € 1 $1 = € 1

____

1.25 $1 = € 1

____

1.25

$25 = €1 × 25

______

1.25 $100 = €

1

____

1.25 × 100

= €20 = €80

Cost €20 Cost €80

+ Labour €50 + Labour €50 Total €70 Total €130

Ans: €70 Ans: €130

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1916LCOL3Bk2SolutionsChapter5resources-1916 LC OL 3 Bk 2-1916_LCOL3_Bk2_Solutions_Ch05