Polygons

6 Polygons

Paper 1

∴ p°

= 120° − 30° − 30° p = 60

1.

J

H

120°

K

Answer: C 4.

G

K

E

x °

n°

E

∠ JKE = =

F

F

6 = 120° ∴ x° = 180° − 120° x = 60

G

J

H

180° (5 − 2) × –––– 5 = 108° 180° − 108° m° = ––––––––––– 2 m = 36 n° = 180° − 108° n = 72 m + n = 36 + 72 = 108

∠ EFG =

Answer: A 2.

108°

m°

180° × ––––

(6 − 2)

108°

x° + x° + x° + 84° + 84° = 540° 3 x° + 168° = 540° 3 x° = 540° − 168° = 372° 372 x = –––– 3 = 124

∴

Answer: A

Answer: A 5. 3.

120° 30°

100°

x °

H

J

R

Q

170° S

P G

p°

30°

y °

V K

(6 − 2)

y° = 180° − 125° y = 55 x° + 100° + 170° + 90° + 125° + 90° = 720° x° + 575° = 720° x° = 720° − 575° x = 145 ∴ x + y = 145 + 55 = 200

180° × –––– 6

= 120° ∠ HJG

T U

F

E

∠ JHG =

125°

180° − 120° = ––––––––––– 2 = 30°

Answer: C

1

©

Penerbitan Pelangi Sdn. Bhd.

Mathematics

SPM

Chapter 6

6.

S T

(6 – 2) × 180° 6 = 120°

∠ EFG

=

∠ EGF

=

x °

R 54°

y °

P

∠TSR

x° x y° y

= (6 − 2)

180° – 120° 2 = 30°

180° – 42° 2 = 69° x° = 120° – 30° – 69° x = 21

Q

∠ EGM

180° × ––––

6 = 120° = 180° − 120° = 60 = 180° − 90° − 54° = 36

=

Answer: A

2.

∴ x + y =

60 + 36 = 96

E

F x °

2y °

Answer: B K 7.

V

2y °

280°

G

80°

U

x °

2 x °

J

46° 120°

W

x °

P

∠QRS =

(6 − 2)

Q

H

= Refex ∠FGH =

360° – 80° = 280°

S

120°

x° + x° + 2 x° + 2 y° + 2 y° + 280° = 720° 4 x° + 4 y° = 720° – 280° 4( x x° + y° ) = 440° x + y = 110

R

180° × –––– 6

Answer: B

= 120° x° + 46° + 120° + 1 120° 20° = 360° x° + 286° = 360° x° = 360° − 286° x = 74

3.

M q° L

Answer: B

82°

E 74°

K

130°

286°

p°

F

50°

H

J

G

∠ JHM = =

180° – 130° = 50°

Paper 1

Refex ∠ JKL =

1.

360° – 74° = 286°

H x ° G

M

69°

p° + q° + 50° + 82° + 286° 286° = 540° p° + q° + 418° = 540° p° + q° = 540° – 418° p + q = 122

J

30° 120° F

42°

K

Answer: A E

©


2

Mathematics

4.

Chapter 6

y° = 360° – 135° – 120° y = 105

S R

SPM

T

x °

Answer: B

72°

O

72°

W

y

°

V

7.

U

G H

360° ∠ ROS = ––––

120° 110°

5 = 72°

p °

x° = 2 × 72° = 144°

F

q°

70°

E

110°

360° ∠TVU = ––––

J

K

5 = 72°

∠ HJE = =

180° − 110° = 70°

y° = 180° – 72° – 72° = 36°

p° + q° + 70° + 110° 110° + 120° = 540° p° + q° + 300° = 540° p° + q° = 540° − 300° p + q = 240

∴ x°

+ y° = 144° + 36° x + y = 180

Answer: D

Answer: D 5.

J E 60°

8.

K

80°

x °

K

M

J

23° x °

H 74°

L

46° F

G

70°

∠GFJ =

180° – 60° – 74° = 46° Given ∠GFJ = = 2∠ EFJ 46° ∠ EFJ = –––– 2 = 23° ∴ x°

60°

120° F

E

H

G

360° = –––– 6 = 60° ∠ LFG = 180° − 60° = 120° ∠ EFL

= 180° − 80° – 23°

180° – 120° –––––––––– 2 = 30° ∠FLM = = 180° − 30° = 150° ∠FLG =

x = 77 Answer: C 6.

30°

150°

K

L y °

J 135°

M

x° = 360° – 70° – 150° – 60°

N P

x = 80

120°

Answer: A H G ∠ EML

Q

E F

9.

R

(8 – 2) × 180° 8 = 135°

R

Q

=

P

S 108° 36°

(6 – 2) × 180° 6 = 120°

∠ EMN =

T y °

U

3

©

V


Mathematics

∠STP =

SPM

Chapter 6

180° × ––––

(5 − 2)

y° + 45° + 45° + (360° − 135°) y° + 315° y° y

5

= 108° 180° − 108° ∠PST = ––––––––––– 2

= 360° = 360° = 360° − 315° = 45

Answer: A

= 36° ∴ y = 36

3.

F

Answer: B

L n°

E

G

72° 30° m°

72°

H

Paper 1 1.

36°

J

K

360° ∠ EJK = ––––

5 = 72° ∠ JKE = 180° − 72° − 72° = 36°

K J

L

90°

M

60°

x °

35°

Q

m° + n° + (36° + 30°) = 180° m° + n° = 180° − 66° m + n = 114

P N

Answer: B

360° = –––– 6 = 60° ∠PJK = 180° − 60° = 120° ∠ JPM = ∠ LMP 540° − 120° − 120° − 120° = ––––––––––––––––– ––––––––––––––––––––––– –––––– 2 = 90° ∠ JPQ = 180° − 35° − 60° = 85° ∴ x° = 90° + 85° x = 175 ∠PJQ

4.

K 60°

p°

60°

F

J 125°

E p°

G

H

180 3 = 60°

∠ LFE = ––––

p° + p° + 60° + 125° + 90° = 2 p° + 275° = 2 p° = p =

Answer: C 2. T 45°

L

540° 540° 540° − 275° 132.5

Answer: C

y °

J K

H 135°

5.

45°

L

R

G

M

Q m°

F

V

S

E

50°

P

360° = –––– 8 = 45° ∠ JHG = 180° − 45° = 135° ∠ HGT

©


T

∠ RST =

(5 − 2)

= 108°

4

180° × –––– 5

U

Mathematics

∠TSV = ∴

180° − 50° = 130° m° = 360° − 108° − 130° m = 122

y °

P

60°

Q

y °

150°

R

× ––––

720° – 4(150°) = ––––––––––––– 2 = 60° ∴ y° + 60° = 150° y° = 150° − 60° y = 90 ∠QPU

Answer: C

Answer: B

10.

7.

U 70°

J

22.5°

T

Sum of angles of PQRSTU = (6 − 2) × 180° = 720°

The number of sides of the regular polygon = 9

K

U

S

180° = 140° n 360° = 140° 180° − –––– n 360° 180° − 140° = –––– n 360° 40° = –––– n 360° n = –––– 40° =9 (n − 2)

Chapter 6

9.

Answer: A 6.

SPM

45° x °

H

P

70° 110°

y °

L

m° n°

Q G

T

105°

R

S

∠TUQ

= ∠PQU = 70° ∠ RQU = = 180° − 70° = 110°

F

M E

∠ JKL =

= y = = =

(8 − 2)

180° × ––––

Sum of angles of QRSTU = (5 − 2) × 180° = 540°

8

135° ∠ JKG 180° − 135° 45°

m ° + n° + 1 110° 10° + 70° + 105° = m° + n° + 285° = m° + n° = m + n =

180° − 135° = ––––––––––– 2 = 22.5° x° = 135° − 45° − 22.5° x = 67.5° ∴ x + y = 67.5 + 45 = 112.5 ∠ MKL

Answer: C 11. L M

J

Answer: B

40°

K x °

8.

540° 540° 540° − 285° 255

y °

360° –––– = 36° n n = 10

108° 36°

N

P

The number of sides of the regular polygon = 10 Answer: B

Q

5

©


Mathematics

SPM

Chapter 6

x° = 180° − 40° x = 140 180° ∠KPN = (5 − 2) × –––– 5 = 108° 180° − 108° ∠ MPN = ––––––––––– 2 = 36° y° = 108° − 36° y = 72 ∴ x + y = 140 + 72 = 212

14.

L

135°

P 45°

N

S Q R

∠PML =

40°

T

Q

(6 − 2)

180° × –––– 6

= 120° ∠PMN = 180° − 120° = 60° 180° ∠ HPQ = (8 − 2) × –––– 8 = 135° ∠PQN = 180° − 135° = 45° ∠ MPQ = 360° − 120° − 135° = 105°

U

S

R

= (5 − 2)

E

y °

M

100°

∠ RQU

120° 60°

40°

x °

F

H

V

P

G

K

Answer: D 12.

J

y° + 60° + 105° + 45° 45° = 360° y° + 210° = 360° y° = 360° − 210° y = 150

180° × ––––

5 = 108° ∠PQU = 180° − 80° = 100° ∴ x° = 360° − 100° − 108° x = 152

Answer: C 15.

F

E

Answer: D 30° y °

13.

W

L G

V

P

U x °

60°

J

H 108°

Q

108°

T

Z

72°

∠FGJ

y °

95°

S

R

∠FGE

180° × ––––

∠PQZ =

(5 − 2)

= ∠ RQZ = = ∠QZS = =

108° 180° − 108° 72° 360° − 108° − 108° 144°

5

y° + 95° + 72° + 144° y° + 311° y° y

∠ EGJ ∠ JGH

y° y x° x ∴ x + y

= 360° = 360° = 360° − 311° = 49

Answer: A

©


= (6 − 2)

6 = 120° 180° − 120° = ––––––––––– 2 = 30° = 120° − 30° = 90° = 180° − 90° = 90° = 180° − 30° = 150 = 180° − 60° − 90° = 30 = 30 + 150 = 180

Answer: B

6

180° × ––––

K

Polygons

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