Polygons: Paper 1

6
Polygons
Paper 1
1.
p = 120 30 30
p = 60
120
Answer: C
4.
180
JKE = (6 2)
6
= 120
x = 180 120
x = 60
108
180
EFG = (5 2)
5
= 108
180 108
m =
2
m = 36
n = 180 108
n = 72
m + n = 36 + 72
= 108
2.
x + x + x + 84 + 84 = 540
3x + 168 = 540
3x = 540 168
= 372
372
x =
3
= 124
Answer: A
Answer: A
5.
120
x
G
y
V
100
170 S
30
K
H
30
p
Answer: A
3.
108
125
U
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
JHG = (6 2)
6
= 120
180 120
HJG =
2
= 30
Answer: C
1
Penerbitan Pelangi Sdn. Bhd.
Mathematics SPM Chapter 6
6.
EFG = (6 2) 180
6
= 120
S
T
54
y
EGF = 180 120

2
= 30
EGM = 180 42
2
= 69
x = 120 30 69
x = 21
180
TSR = (6 2)
6
= 120
x = 180 120
x = 60
y = 180 90 54
y = 36
Answer: A
2.
x + y = 60 + 36

= 96
Answer: B
K
7.
2y
2y
80
x
120
x
2x
46
W
280
Reflex FGH = 360 80

= 280
x + x + 2x + 2y + 2y + 280 = 720

4x + 4y = 720 280

4(x + y) = 440
x + y = 110
120
R
180
QRS = (6 2)
6

= 120
Answer: B
x + 46 + 120 + 120 = 360

x + 286 = 360
x = 360 286
x = 74
3.
M
q
Answer: B
82
74
E
K
F
130
286
p
J
50
H
JHM = 180 130

= 50
Paper 1
1.
Reflex JKL = 360 74

= 286
H
x
69
30
p + q + 50 + 82 + 286 = 540

p + q + 418 = 540

p + q = 540 418

p + q = 122
120
F
42
Answer: A
4.
y = 360 135 120

y = 105
S
R
Answer: B
72
72
360
ROS =
5

= 72
7.
120
110

x = 2 72
= 144
q
110
360
TVU =
5

= 72
70
HJE = 180 110

= 70

y = 180 72 72
= 36
p + q + 70 + 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
60
74
8.
E
80
23
H
46
70
y
M
x = 360 70 150 60
N
120
x = 80
Answer: A
Q
E
G
180 120
FLG =
2

= 30
FLM = 180 30

= 150
120
F
360
EFL =
6

= 60
LFG = 180 60

= 120
Answer: C
135
J
30
60
x = 77
L
150
x = 180 80 23
GFJ = 180 60 74
= 46
Given GFJ = 2EFJ
46
EFJ =
2
= 23
6.
9.
EML = (8 2) 180
8
= 135
EMN = (6 2) 180
6
= 120
S
36
108
T
y
U
180
STP = (5 2)
5
= 108
y + 45 + 45 + (360 135) = 360

y + 315 = 360
y = 360 315
y = 45
180 108
PST =
2
= 36
y = 36
Answer: A
3.
Answer: B
L
E
72
Paper 1
1.
60
90 x
35
4.
135
60
125
p + p + 60 + 125 + 90 = 540
2p + 275 = 540
2p = 540 275
p = 132.5
Answer: C
H
45
5.
R
Q
m
50
360
HGT =
8

= 45
JHG = 180 45

= 135
180
LFE =
3

= 60
G
M
36
L
60
Answer: C
72
Answer: B
360
PJQ =
6
= 60
PJK = 180 60
= 120
JPM = LMP
540 120 120 120
=
2
= 90
JPQ = 180 35 60
= 85
x = 90 + 85
x = 175
45
m + n + (36 + 30) = 180

m + n = 180 66
m + n = 114
2.
30
360
EJK =
5

= 72
JKE = 180 72 72

= 36
K
L
180
RST = (5 2)
5
= 108
9.
TSV = 180 50
= 130
m = 360 108 130
m = 122
P
Q
Answer: A
60
y
150
180 = 140
6. (n 2)
n
360
180 = 140
n
360
180 140 =
n
360

40 =
n
360
n =
40
= 9
720 4(150)
QPU =
2
= 60
y + 60 = 150
y = 150 60
y = 90

Answer: C
Answer: B
10.
7.
22.5
Sum of angles of PQRSTU

= (6 2) 180
= 720
The number of sides of the regular polygon = 9
J
45
x
U
70
70 110
Q
G
M
m
n
R
105
S
TUQ = PQU

= 70
RQU = 180 70

= 110
180
JKL = (8 2)
8
= 135
y = JKG
= 180 135
= 45
Sum of angles of QRSTU

= (5 2) 180
= 540
m + n + 110 + 70 + 105 = 540

m + n + 285 = 540
m + n = 540 285
m + n = 255
180 135
MKL =
2
= 22.5
x = 135 45 22.5
x = 67.5
x + y = 67.5 + 45
= 112.5
Answer: C
11.
Answer: B
L
J
40
360 = 36
8.
n
n = 10
K
y
108
36
N
The number of sides of the regular polygon = 10

Answer: B
14.
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
40
40
100
120
y
P
45
15.
V
108
Z
x
H
108
30
L
60
J
180
FGJ = (6 2)
6
= 120
180 120
FGE =
2
= 30
EGJ = 120 30
= 90
JGH = 180 90
= 90
y = 180 30
y = 150
x = 180 60 90
x = 30
x + y = 30 + 150
= 180
T
S
180
PQZ = (5 2)
5

= 108
RQZ = 180 108

= 72
QZS = 360 108 108

= 144
y + 95 + 72 + 144 = 360
y + 311 = 360
y = 360 311
y = 49
Answer: A
95
Answer: C
72
Answer: D
135
y + 60 + 105 + 45 = 360
y + 210 = 360
y = 360 210
y = 150
180
RQU = (5 2)
5
= 108
PQU = 180 80
= 100
x = 360 100 108
x = 152
13.
180
PML = (6 2)
6
= 120
PMN = 180 120
= 60
180
HPQ = (8 2)
8
= 135
PQN = 180 135
= 45
MPQ = 360 120 135
= 105
60
M
V
P
G
H
Answer: D
12.
J
K
Answer: B
6

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6

x + 100 + 170 + 90 + 125 + 90 = 720

Penerbitan Pelangi Sdn. Bhd.

Mathematics SPM Chapter 6

EGF = 180 120

Reflex FGH = 360 80

x + 46 + 120 + 120 = 360

JHM = 180 130

Reflex JKL = 360 74

Penerbitan Pelangi Sdn. Bhd.

Mathematics SPM Chapter 6

y = 360 135 120

HJE = 180 110

p + q + 70 + 110 + 120 = 540

Penerbitan Pelangi Sdn. Bhd.

Mathematics SPM Chapter 6

y + 45 + 45 + (360 135) = 360

Penerbitan Pelangi Sdn. Bhd.

m + n + (36 + 30) = 180

Mathematics SPM Chapter 6

Sum of angles of PQRSTU

The number of sides of the regular polygon = 9

Sum of angles of QRSTU

m + n + 110 + 70 + 105 = 540

The number of sides of the regular polygon = 10

Penerbitan Pelangi Sdn. Bhd.

Mathematics SPM Chapter 6

Penerbitan Pelangi Sdn. Bhd.

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