Polygons - Multiple Choice Questions

Multiple-choice Questions 3 In the diagram, ABCDE is a 5 In the diagram, P, Q, R, S and U
regular pentagon and BCJHGF is
(PAPER I) a regular hexagon. are five successive vertices of a
regular octagon.
1 In the diagram, PQRST is a H RST and PUT are straight lines.
regular pentagon. PQU and TSV
are straight lines. p ,,,,,

V Q

Yo K

s Find the value of x.
A 36
TR B 38 Find the value of z.
C 42
2yo D 48 A 12.5 C 22.5

pQ u 4 In the diagram, PQRST is a B 17.5 D 25
regular pentagon and M is the
Find the value of y. midpoint of ST. 6 In the diagram, PQRSTU is a
A 48 regular hexagon and PRW is a
B 50 p straight line.

C 56 p

D 64

2 In the diagram, PQRSTU is a u
regular hexagon. QRW and QSV
are straight lines. QT
T
QR

p Rs

UT Find the value of y. Find the value of x.
A 120 A 28
Find the value of x + y. B 128 B 30
C 130 C 32
A 146 C 170 D 132 D 35

B 160 D 180

7 In the diagram, PQRST is a In the diagram, STUV is a 15 The diagram shows a regular
regular pentagon. PQUV and SRU rhombus. RST and PVT are
are straight lines. straight lines. Kl pentagon and a regular octagon.

s XO p [·os MQR and MZY are straight lines.

T Vu

X

T

pQ u V XO y

Find the value of x. Rs T s

A 41 C 54 Find the value of x + y.

B 45 D 59 A 210 C 230 QR

8 In the diagram, PQRS is a B 225 D 355

l'rl parallelogram. 12 In the diagram, PQR is an Find the value of n.
<ilw equilateral triangle. PTS and QRS
\'14_. u A 106 C 126
are straight lines.
B 116 D 136
p
16 In the diagram, PQRST is
sr-'. ' regular pentagon.
M is the midpoint of ST.
R QR
p

S

Find the value of x + y. Given that PR = PT, find the value

A 90 C 130 of X + y. QT

B 100 D 280 A 80 C 120

9 In the diagram, P, Q, R, S and T are B 100 D 140
five successive vertices of a regular
polygon. RSU is a straight line. 13 In the diagram, PQRS is a rhombus. Rs
QST and QPV are straight lines.

' V Find the value of y - x.
p,
A 24 C 32

B 30 D 36

Q 17 The diagram shows a regular
a'iilt hexagon PQRSTU. TUV and TPW
0( ,L CT '.[~ are straight lines.

RS u

Find the value of y. -- 0.~-~R

A 36 C 54 R w

B 48 D 72 Find the value of y - x.

10 In the diagram, PQRS is A 20 C 70 s
a rhombus and QUVS is a
parallelogram. B 60 D 80

c-----,-.p 14 In the diagram, PQRSTU is a X°
regular hexagon and PQGHK is a
regular pentagon. Vu T

Find the value of x.

T A 35 C 55

B 45 D 75

Rl l I ''"

18 In the diagram, PQRSTU is a

regular hexagon and TUV is a

straight line.

V Q W "s X0

Find the value of x + y. Find the value of y. p
y•
A 70 C 90 A 24 C 48
B 46 D 56
8 80 D 100

RQ

-,

Find the value of x - y. Vu 26 In the diagram, PQR, PWV and
A 15
B 20 GI UTS are straight lines
C 25
D 35 '03 '

19 In the diagram, PQR and TUV are T
y
&SI straight lines.
s
'•10
'II M QR w XO 120°

Find the value of m + n.

A 195 C 243 pR

B 234 D 279

s The diagram shows an irregular Given that WP = WQ, find the
Rtl polygon.
V value of y - x.
us
A 130 C 170

B 150 D 180

yo R 27 In the diagram, PQRST is a
p regular pentagon. VPQ and VUR

Find the value of x + y. 0·41 are stra1.ght 1m· es.

A 100 C 120 p Yo s

B 110 D 130

20 In the diagram, PQRST is a Q R

ml regular pentagon and XQR is a Find the value of x + y.

'.'11 straight line. A 120 C 260

V B 130 D 390

24 The diagram shows a regular V
hexagon PQRSTU with centre 0.
T Find the value of x + y.
'12 QPV and SUV are straight lines.
A 46 C 56
R
ps B 52 D 66

28 In the diagram, PQR is parallel to

Q R s UT.

Find the value of m. ~OS ' T
A 96
B 104 Yo
C 106
sXO
D 116
V 115°
pR
Find the value of x + y.
21 In the diagram, P, Q, R, S and T
A 120 C 140 Find the value of x + y.
are five successive vertices of a
B 130 D 150 A 190 C 245
regular polygon.
B 225 D 255
25 In the diagram, PQRSTU is a
29 In the diagram, PQRS is a
l l regular hexagon, WPQ and VUP I~ rhombus.

~~3_ are straight lines. p

V

p

QR R

Find the value of x.

A 95 C 115 Q R

B 105 D 150 p Find the value of y.

22 The di agram shows a regular Find the value of x + y. A 18 C 54
pentagon and a regular octagon.
MQR and MZY are straight lines. A 66 C 76 B 36 D 72

B 72 D 114

II30 In the diagram, PQRST is a Tu
regular pentagon and PRUV is a
'06 parallelogram. s

su R

R Q
V
Find the valu
Qp A 85
B 95
Find the value of x. C 105
A 114 D 115
B 128
C 140 32 In the diagram
D 148
&fl parallelogram
31 In the diagram, PQRSTUVW is a
B,'ol regular octagon and MNPQ is a J>7! straight line.
'.Q?. straight line.
Q
2xo {

R1

u Find the value of x + y.

V A 195
B 205
w C 215
D 250
ue of x.
33 In the diagram, PQRST is a

1fi1 regular pentagon and PU= PV.

'08

s

m, PQRS is a RT
m and RST is a
Find the value of x.
w A 39
B 70
p C 71
yo V D 73

s{I ..JV {\

T