ANSWERS 681
ex= 100 fcorresponding anglesg
fx=49fco-interior anglesg
gx= 112 fvertically opposite anglesg
hx=45fangles at a pointg
i d= 333 fangles at a pointg
j a= 116 fcorresponding anglesg
kx= 138 fangles on a lineg
l b= 108 falternate anglesg
ma=65fangles on a lineg,b=65fcorresponding anglesg
na=57fvert. opp. anglesg,
b=57fcorresponding anglesg
oa= 102fco-interior anglesg,b= 102fco-interior anglesg
pc=90 fangles on a lineg
qa=59fangles on a lineg,b=59fcorresponding anglesg
ri= 218 fangles at a pointg
sa= 122fvert. opp. anglesg,b=58fco-interior anglesg
c=58fcorresponding anglesg,d= 122fangles on a lineg
tb= 137 fangles at a pointg
ur=81, s=81 fcorresponding anglesg
3ad= 125 fangles at a pointg
be= 120 fangles at a pointg
cf=45fangles at a pointg
dh=36fangles on a lineg
eg=60fcorresponding angles/angles on a lineg
fx=85fco-interior anglesg
gx=45fangles on a lineg
hx=15fangles in right angleg
i x=42fangles at a pointg
4aKLkMN falternate angles equalg
bKL,MN fco-interior angles not supplementaryg
cKLkMN fcorresponding angles equalg
5ax=60,y=60 ba=90,b=35
cp=90, q=25,r=25
EXERCISE 4B
1aa=62 fangles of a triangleg
bb=91 fangles of a triangleg
cc= 109 fangles of a triangleg
dd= 128 fexterior angle of a triangleg
ee= 136 fexterior angle of a triangleg
ff=58fexterior angle of a triangleg
2aAB b AC c BC dAC and BC eBC
fBC gBC hBC i AB
3atrue b false c false dfalse e true
4aa=20 fangles of a triangleg
bb=60 fangles of a triangleg
cc=56 fcorresponding angles/angles of a triangleg
d=76 fangles of a triangleg
da=84fvert. opp. anglesg,b=48fangles of a triangleg
ea=60 fangles on a lineg
b= 100 fext. angle of a triangleg
fa=72, b=65fvertically opposite anglesg
c= 137 fext. angle of triangleg
d=43 fangles on a lineg
546 : 5 o, 34 : 5 oand 99 o
EXERCISE 4C
1ax=36fisosceles triangle theorem/angles of a trianglegbx=55fisosceles triangle theorem/angles of a triangleg
cx=36fisosceles triangle theorem/angles of a triangleg
dx=73fisosceles triangle theoremg
ex=60fangles on a line/isos.¢theorem/angles of a¢g
fx=32: 5 fisos.¢theorem/angles on a line/angles of a¢g
2ax=16fisosceles triangle theoremg
bx=9 fisosceles triangle theoremg
cx=90fisosceles triangle theorem/
line from apex to midpoint of baseg
3aequilateral b isosceles cequilateral d isosceles
eequilateral f isosceles
4ax=52 b ¢ABC is isosceles (BA=BC)
5aμ=72 b Á=54 cAbBC= 108o
6aμ=36 b Á=72 cAbBC= 144o
EXERCISE 4D
1a 360 o b 540 o c 720 o d 1080 o
2ax=87 b x=43 cx=52: 5 d a= 108
ea= 120 f a=65
3ax=60fangles of a pentagong
bx=72fangles of a hexagong
cx= 120 fangles of a hexagong
dx=60fangles of a hexagong
ex= 125 fangles of a heptagong
fx= 135 fangles of an octagong
4135 o 5a 108 o b 120 o c 135 o d 144 o
612 angles 7 No such polygon exists.
8 Regular
PolygonNo. of
sidesNo. of
anglesSize of
each angle
equilateral triangle 33 60o
square 44 90o
pentagon 5 5 108 o
hexagon 6 6 120 o
octagon 8 8 135 o
decagon 10 10 144 o9 ² 180(n¡2)o ² μ=180(n¡2)o
n
10 a Yes, these are all 30 o. bYes, the two inner ones.
11 a 12847 o b®=25^57 , ̄= 102^67 ,°=77^17 , ±=51^37
12 ®=60, ̄=80
13 We must be able to find integersksuch that
kh(n¡2)£ 180
ni
= 360 fangles at a pointg) k=
2 n
n¡ 2
wheren=3, 4 , 5 , 6 , ......
The only possibilities are:
k=6, n=3; k=4,n=4; k=3,n=6
So, only equilateral triangles, squares and regular hexagons
tessellate.
14 a bIB MYP_3 ANS
cyan magenta yellow black(^05255075950525507595)
100 100
(^05255075950525507595)
100 100
Y:\HAESE\IGCSE01\IG01_an\681IB_IGC1_an.CDR Tuesday, 18 November 2008 2:35:57 PM PETER