2 Arrange the following angles in order from smallest to largest. A B C D E F. 3 List the pairs of angles which look to be the same size.

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2 I n rcnt yars thr has bn an xplosion in rsarch basd on dinosaur tracks. Using trackways w can tll whthr a dinosaur was walking, trotting, running or wading. W can stimat its spd by looking at th lngth of th strid and th stp angl. Dinosaurs, lik humans, ar diagonal walkrs, which mans a lin drawn btwn th hls of opposit footprints is at an angl to th dirction of travl. Othr important masurmnts includ th angl mad btwn th innrmost and outrmost tos, and track rotation, which masurs th dgr to which tracks ar turnd inward (pigon-tod) or outward (duck-footd). hi.com.au 139

3 Worksht R5.1 Prpar for this chaptr by attmpting th following qustions. If you hav difficulty with a qustion, click on th Rplay Worksht icon on your Maths Zon CD or ask your tachr for th Rplay Worksht. 1 Stat th valu indicatd by (a) ach arrow in th following diagram. (b) (d) Worksht R5.2 (c) 2 Arrang th following angls in ordr from smallst to largst. A B C D E F Worksht R5.3 3 List th pairs of angls which look to b th sam siz. A B C D E F 140 acut angl complmnt complmntary dgr MATHS ZONE 7 obtus angl protractor rflx angl rvolution right angl straight angl supplmnt supplmntary vrtx vrtically opposit

4 An angl is formd whnvr two or mor lins mt (or intrsct). Th cornr formd whr th lins mt is calld th vrtx. Two angls ar shown blow. 1 3 On is lss than -- of a turn and th othr is gratr than -- of a turn. 4 4 If you ar going to masur th siz of th angl it is important to b clar about which of th two angls you ar going to masur. That is why it is important to mark th actual angl rquird. Th lins which mt to mak th angl ar somtims calld th arms of th angl. Th siz of an angl is th amount of turn from on arm of th angl to th othr. W us th unit dgr ( ) to dscrib th siz of an angl. Thr ar 360 in a full circl. Othr usful angls to rmmbr ar a quartr turn (of a full circl) which is 90 and a half turn (of a full circl) which is 180. W us a protractor to masur th siz of angls. Using a smi-circular protractor Som protractors ar smi-circular, and hav two scals markd from 0 to 180 only. Th two scals ar for masuring angls facing diffrnt ways, but can b confusing. Tutorial Using a smi-circular protractor is slightly complicatd, and th stps followd dpnd on th typ of angl. You must also dcid which of th two scals to us. 5 angls 141

5 For angls lss than 180 : 1. Plac th cntr of th protractor s bas on th vrtx. 2. Lin up th bas of th protractor with on of th arms of th angl. 3. Us th scal on th protractor bas that starts at 0, and rad th numbr of dgrs th angl spans. (It may b ncssary to xtnd th angl s arms.) A 60 angl. Notic how th innr scal is usd, bcaus this is th on that has 0 on th bottom arm of th angl. For angls gratr than 180 : 1. Masur th othr sid angl as shown using th mthod dscribd abov. Th othr sid angl in our xampl hr masurs dsird angl start at 0 start at othr sid angl A 125 angl facing th othr way. This tim th outr scal is usd. 2. Subtract this othr sid angl from 360 to find th dsird angl start at 0 Using a circular protractor A circular protractor markd from 0 to 360 is shown opposit. To masur an angl with a circular protractor: 1. Plac th cntr dot of th protractor on th vrtx. 2. Lin up th horizontal 0 cntr-lin of th protractor with on of th arms of th angl. (You may hav to turn around th angl to do this.) This angl masurs MATHS ZONE 7

6 3. Rad whr th othr arm of th angl cuts th outr scal of th protractor. (It may b ncssary to xtnd th angl s arms.) This angl masurs It is asy to mak a mistak whn using a protractor and us th wrong scal. You should always mak an stimat of th angl bfor masuring it. You can thn mak sur your masurmnt of th angl is rasonabl. Somtims whn you go to masur th siz of an angl you find that th arm of th angl is too short to pass through th scal on th protractor. Whn this occurs you can just xtnd th lngth of th arm. This dos not chang th siz of th angl. Us a rulr and b carful that th lin is straight. Tutorial xrcis 5.1 Cor Masuring angls Prparation: Prp Zon Q1 1 Us a protractor to masur th siz of th following angls. Writ your answr to th narst dgr. (a) (b) hi.com.au You will nd a protractor. (c) 5 angls 143

7 (d) () (f) (g) (h) 2 Us a protractor to masur th siz of th following angls. Writ your answr to th narst dgr. (a) (b) (c) (d) () (f) 144 MATHS ZONE 7

8 3 Us a protractor to masur th siz of th following angls. Writ your answr to th narst dgr. (a) (b) Worksht C5.1 (c) (d) () 4 Us a protractor to masur th siz of th following angls. Writ your answr to th narst dgr. (a) (b) (c) (d) 5 angls 145

9 5 Us a protractor to masur th siz of th following angls. Writ your answr to th narst dgr. (a) (b) (c) (d) () (f) (g) (h) 146 MATHS ZONE 7

10 Extnsion 6 Choos th corrct answr. Whn you masur th siz of th angl btwn th laddr and th wall in th photo, you find it is: A 150 B 48 C 33 D 27 7 Masur th angl of ascnt (th angl btwn th flight path and th runway) for th aircraft in th diagram blow. 8 Masur th angl of lvation ( ) to th mountain top in th diagram. 9 Choos th corrct answr. Whn you masur th angl of dprssion (d ) to th ship in th diagram, you find it is: A 50 B 40 C 140 D 130 d 5 angls 147

11 10 Tigr plans his assault on a particular golf hol by drawing th idal path that his ball should tak. hol What is th siz of th angl btwn th two idal paths? Qustions Qustions Count th angls How many angls can you count in th diagram? Masur ach on. Thr ar mor angls hr than you may think. Don t forgt th big ons. Do ths in your had as quickly as you can and writ down th answrs. Tim targt: 2 minuts of What is th siz of ach angl aftr a straight angl has bn dividd into 3 qual angls? 8 How many 25c lollis can you buy for $4.00? 9 If you slp for 7 hours, how many minuts do you slp for? 10 If a = 5, find a MATHS ZONE 7

12 Now that you hav had xprinc using a protractor to masur angls, you should b bttr at giving rough stimats of th siz of angls without using a protractor. Whn stimating angls, try to visualis a 360 circular protractor and think about how much of th complt circl you hav covrd Tutorial xrcis 5.2 Estimating angls Prparation: Prp Zon Q1 3, Ex 5.1 In this xrcis, do not us a protractor unlss spcifically askd to. Rfr to a diagram of a circular protractor if ncssary to hlp you. Cor 1 List th following angls in ordr of incrasing siz (i.. smallst to largst). (a) A B C D Intractiv 5 angls 149

13 (b) A C D B 2 Choos th corrct answr. (a) Th angl shown hr is about: A 20 B 45 C 60 D 85 (b) Th angl shown hr is about: A 100 B 145 C 185 D 200 (c) Th angl shown hr is about: A 190 B 230 C 280 D 310 (d) Th angl shown hr is about: A 60 B 120 C 240 D Choos th corrct answr. (a) Which of th angls blow is about 170? A B C D 150 MATHS ZONE 7

14 (b) Which of th angls blow is about 265? A C D B (c) Which of th angls blow is about 5? A B C D (d) Which of th angls blow is about 330? A C D B 4 Estimat th siz of ach of ths angls. Copy th tabl on th following pag and complt only th first column. (a) (b) (c) (d) () (f) (g) (h) (i) (j) 5 angls 151

15 Angl Estimat Masurd valu Error (a) (b) (c) (d) () (f) (g) (h) (i) (j) Total rror Avrag rror (Divid total rror by 10) Extnsion 5 Now masur ach of th angls in Qustion 4 using a protractor, and complt th tabl. You will nd to xtnd th lngth of th arms. Th rror is th diffrnc btwn your stimat and th masurd valu. It dosn t mattr whthr th stimat is gratr than or smallr than th masurd valu. How dos your angl-stimating ability compar with that of your classmats? Qustions You will nd a protractor. Using a smi-circular protractor 1. If th angl is lss than 180, follow th procdur givn for a circular protractor (blow). 2. If th angl is gratr than 180, procd as follows. An xampl of 200 is usd to xplain th procdur. Calculat th othr sid angl by subtracting from MATHS ZONE 7

16 90 3. Draw a bas lin and a vrtx dot. (A vrtx dot marks th location of th angl s cornr.) 4. Plac th protractor upsid down so its zro is on th bas lin and its cntr is on th vrtx dot. 5. Locat 160 (start at 0 on th bas lin and mov clockwis) and mark a small dot on th dg of th scal as shown. 6. Rmov th protractor and join th small dot to th vrtx dot. 7. Mark th othr sid of th angl drawn, as this is th angl dsird Using a circular protractor 1. Draw a bas lin and a vrtx dot. 2. Plac th zro of th protractor on th bas lin with its cntr on th vrtx dot. 3. Locat th dsird angl (.g. 75 ) and mark a small dot on th dg of th scal as shown vrtx bas lin small dot opposit dsird angl Rmov th protractor and join th small dot to th vrtx dot. 5. Mark th angl with a small arc as shown. A pro-tractor rally 75 5 angls 153

17 xrcis 5.3 You will nd: A protractor. Drawing angls with a protractor Prparation: Prp Zon Q1, Ex 5.1 Cor 1 Draw th following angls using a protractor. (a) 10 (b) 70 (c) 6 (d) 36 () 55 (f) 84 2 Draw th following angls using a protractor. (a) 95 (b) 151 (c) 130 (d) 100 () 175 (f) Draw th following angls using a protractor. (a) 182 (b) 260 (c) 222 (d) 205 () 235 (f) Draw th following angls using a protractor. (a) 290 (b) 318 (c) 275 (d) 334 () 300 (f) 247 Extnsion 5 Draw th following angls without a protractor. (a) 180 (b) For ach of th following draw a circl thn divid it into wdgs with th following angls at th cntr. (a) 100, 210, 50 (b) 90, 90, 72, 108 (c) 40, 140, 180 (d) 32, 161, 85, 82 () 215, 34, 71, 40 (f) 19, 28, 172, 141 Worksht C5.2 No, I said draw an angl. Ella s angls Ella nds to draw a 60 angl, but sh has lost hr protractor. Sh has a stncil that can draw 90 and 40 angls. How can sh us ths two angl sizs to draw a 60 angl? Ella will nd to us a sris of stps to construct hr angl. 154 MATHS ZONE 7

18 Dot papr angls Worksht A5.1 You will nd squar grid dot papr, a pncil and rulr. 1 Draw as many diffrnt angls as you can on sparat 3 3 dot grids so that ach angl starts and nds on a dot and has its cornr (vrtx) on a dot. On xampl is shown opposit. Us a protractor to masur ach angl and writ th numbr of dgrs nxt to ach on. Did you find th tn diffrnt possibl angls? If you found mor than tn, chck carfully som of your angls may actually b th sam siz. You may lik to work with a partnr to mak sur all possibl angls ar found. 2 Choos on of th angls from Qustion 1 and, on a nw 3 cm 3 cm grid, draw this angl in as many diffrnt positions as possibl. You may wish to colour th rsulting pattrn. Th pattrn for on of th angls is shown opposit. G, it s going to b a bit hard to draw this on dot papr. 3 Try Qustion 2 for svral of th othr angls. 4 Invstigat th possibl angls for a largr (.g. 4 4) grid, and try to produc som pattrns using rpatd angls. 5 angls 155

19 Billiard ball bouncs Worksht A5.2 It is oftn said that a prson s skill at billiards or pool is a sign of misspnt youth, but top playrs could claim to hav workd hard at thir maths. Th gam of billiards originatd in Franc in th arly 1500s. First a railing was addd to th dgs, thn a cushion in 1835, allowing playrs to bounc th ball off th sids with spd and accuracy. Th objct of th gam was to us th whit ball to hit both th rd ball and th spot ball with th sam shot this was calld a cannon. Th modrn gam was dvlopd latr by th British and uss a 12 foot by 6 foot tabl (3.66 m by 1.83 m). Important in planning shots is th fact that a ball bouncs off a sid at th sam angl at which it approachs. Qustions Imagin a 6 4 billiard tabl with pockts at th cornrs only, and a ball hit from a cornr at an angl of 45 to a sid of th tabl. Assuming that: th rbound angl quals th approach angl for ach collision th ball maks with a sid of th tabl, and th ball dosn t stop rolling until it falls into a cornr pockt, th path of th ball can b tracd as shown. You will nd cntimtr grid papr, blank papr, a protractor, rulr and pncil. 1 On squar cntimtr grid papr, draw tabls of th dimnsions givn, and trac th path of a ball hit from a cornr at an angl of 45 to a sid until th path nds at a pockt. (a) 1 cm 4 cm (b) 2 cm 8 cm (c) 3 cm 12 cm (d) 3 cm 4 cm () 9 cm 12 cm (f) 5 cm 6 cm (g) 4 cm 5 cm (h) 8 cm 10 cm 156 MATHS ZONE 7

20 (i) 3 cm 8 cm (j) 5 cm 7 cm (k) 4 cm 9 cm (l) 7 cm 9 cm (m) 6 cm 11 cm (n) 5 cm 5 cm 2 Copy and complt th tabl blow using your diagrams from Qustion Tabl dimnsions No. bouncs Tabl dimnsions No. bouncs (a) 1 4 (h) 8 10 (b) 2 8 (i) 3 8 (c) 3 12 (j) 5 7 (d) 3 4 (k) 4 9 () 9 12 (l) 7 9 (f) 5 6 (m) 6 11 (g) 4 5 (n) If you can, xplain how you can prdict: (a) whthr or not th ball will visit vry squar (b) how many bouncs will occur (c) which pockt th ball will nd up in. 4 If you answrd Qustion 3(b), prdict how many bouncs will occur for a tabl. 5 (a) On squar cntimtr grid papr, trac th path of a ball hit from th position shown on a 5 10 tabl. (b) Try starting from diffrnt positions and trac th paths. hi.com.au Activity Us your undrstanding of angls to play a gam of onlin pool at this sit. 5 angls 157

21 Angls may b classifid as on of th following typs: 90 Acut angl: lss than 90 smallr than a squar cornr Right angl: xactly 90 1 a squar cornr, a -- turn. 4 A small squar drawn in th cornr of an angl mans it is a right angl. 90 Obtus angl: mor than 90 but lss than 180 biggr than a squar cornr. 180 Straight angl: xactly 180 a straight lin angl, a half turn. 180 Rflx angl: gratr than 180 but lss than 360 lik th angl on th outsid of a bnt kn Rvolution: 360 a full circl MATHS ZONE 7

22 Naming angls Capital lttrs may b usd to hlp us dscrib angls. Th angl shown may b dscribd as angl ABC, B or ABC. ( is th symbol for angl.) CBA or CBA is also corrct. W can us th sam lttrs to nam points, lins and intrvals. B A C Notic that th lttr on th cornr of th angl (th vrtx) gos in th middl of th thr lttrs. In this cas th B must b in th middl. xrcis 5.4 Dscribing angls Prparation: Prp Zon Q1 and 2, Ex 5.2 Tutorial Cor 1 Stat th typ of angl shown in ach cas. (a) (b) (c) Worksht C5.3 (d) () (f) (g) (h) (i) (j) (k) (l) (m) (n) (o) (p) (q) (r) 5 angls 159

23 (s) (t) (u) 2 Stat th typ of angl givn in ach cas. (a) 23 (b) 117 (c) 275 (d) 360 () 180 (f) 75 (g) 90 (h) Draw two xampls of: (a) an acut angl (b) a rflx angl (c) an obtus angl. 4 Giv a lttr nam for ach of th following angls. (a) Q (b) (c) O 3 S D B Worksht C5.4 P R T A (d) I () S (f) C A T K W H D 5 Draw any angl which may b namd: (a) PQR (b) G (c) K (d) DEF Extnsion 6 Giv th lttr nam of: (a) ach acut angl in th diagram, using thr lttrs (b) ach obtus angl in th diagram, using thr lttrs (c) th point whr CO touchs DA, using on lttr (d) th lin that mts DA at right angls, using two lttrs. 7 (a) Masur th rflx angl RMS in th diagram. (b) Masur th rflx angl P PMS in th diagram. (c) Why is it ncssary to spcify rflx in parts (a) and (b) abov? C D M B O R A S Qustions Homwork 5.1 Worksht A5.3 Worksht A MATHS ZONE 7

24 Complmntary and supplmntary angls Angls on a lin and angls in a right angl hav crtain proprtis. To answr th following qustions, click on th icons to th right to opn th Cabri Gomtry fils on complmntary and supplmntary angls. Obsrv what happns to th sizs of th angls whn you drag th point. You will nd to download Cabri Gomtry from th Maths Zon CD if you havn t alrady don so. 1 What can you say about angls on a straight lin? Ths ar calld supplmntary angls. 2 What can you say about angls in a right angl? Ths ar calld complmntary angls. Intractiv Intractiv Complmntary angls add up to 90 (a right angl). 40 and 50 ar complmntary angls bcaus togthr thy add up to 90. If two angls ar complmntary, w say ach is th complmnt of th othr. For xampl, 40 is th complmnt of 50. A pair of complmntary angls Supplmntary angls add up to 180 (a straight angl). 100 and 80 ar supplmntary angls bcaus togthr thy add up to 180. If two angls ar supplmntary, w say ach is th supplmnt of th othr. For xampl, 100 is th supplmnt of 80. A pair of supplmntary angls angls 161

25 On way of avoiding gtting mixd up with ths dfinitions is to rmmbr that, whn counting, 90 coms bfor 180, and whn rciting th alphabt, C coms bfor S. C 90 workd xampl 1 S 180 (a) What is th complmnt of 11? (b) What is th supplmnt of 57? (c) Find th siz of angl x. (d) Find th siz of angl y. 19 x 78 y Stps (a) An angl and its complmnt must add up to 90, so w subtract 11 from 90 to find th complmnt. (b) An angl and its supplmnt add up to 180, so w subtract 57 from 180 to find th supplmnt. (c) x and 78 ar shown as supplmntary angls, so w subtract 78 from 180 to find x. (d) y and 19 ar shown as complmntary angls, so w subtract 19 from 90 to find y. Solutions (a) Th complmnt of 11 is 79. (b) Th supplmnt of 57 is 123. (c) x = 102 (d) y = 71 Complmntary angls add Supplmntary angls add up to 90 up to 180 b b C 90 S 180 Tutorial 162 MATHS ZONE 7

26 xrcis 5.5 Complmntary and supplmntary angls Cor Prparation: Ex Find th siz of angl x in ach cas. (a) (b) (c) Tstr x x x 76 (d) () (f) x 27 x 67 x 34 (g) (h) (i) x x x 2 Find th complmnt of th following angls. (a) 27 (b) 45 (c) 68 (d) 15 3 Choos th corrct answr. (a) Which on of th following is a pair of complmntary angls? A 330 and 30 B 30 and 150 C 15 and 75 D 60 and 40 (b) Which on of th following is a pair of supplmntary angls? A 0 and 90 B 45 and 55 C 90 and 90 D 200 and 160 (c) Which diagram shows supplmntary angls? A B C D Worksht C5.5 Worksht C5.6 I lik your shirt. (d) Which diagram shows complmntary angls? A B C D A complimntary angl 5 angls 163

27 4 Find th siz of angl y in ach cas. (a) (b) (c) y 5 (d) 30 y () 120 y (f) 37 y y 123 y 25 (h) (g) y (i) y y 5 Find th supplmnt of th following angls. (a) 32 (b) 90 (c) 124 (d) 176 Extnsion 6 Dtrmin th siz of angl in ach cas. (a) (b) (c) (d) () (f) (a) Writ two xampls of pairs of complmntary angls. (b) Writ two xampls of pairs of supplmntary angls. 8 (a) Explain why adjacnt angls adding to 90 form a right angl. (b) Explain why adjacnt angls adding to 180 form a straight angl. Worksht C5.7 Qustions 164 MATHS ZONE 7

28 Answr th following, showing your working, thn arrang th lttrs in th ordr shown by th corrsponding answrs to find th cartoon caption. Th following ar angls in a right angl. Find th valu of th pronumral. 37, n N 56, u U 29, 36, c C 12, 57, l L Th following ar angls on a straight lin. Find th valu of th pronumral. 29, A 142, t T 13, 59, g G 72, 53, E W can s from th circular protractor that thr ar 360 in a rvolution. If mor than on angl can b addd togthr to complt on full rvolution (a circl), thn th angls must add up to 360. b c + b + c = angls 165

29 workd xampl 2 Find th siz of ach of th unknown angls blow. (a) (b) b 61 Stps (a) Subtract th known angl from 360 to find th valu of. Solutions (a) = 322 (b) 1. Add th known angls. (b) Subtract th total of th known angls from 360 to find th valu of b b = 84 xrcis 5.6 Angls in a rvolution Tutorial Prparation: Ex 5.4 Cor 1 Find th valu of th pronumral in ach cas. (a) (b) (c) b c 47 Worksht C5.8 (d) () (f) 215 f 158 d 310 (g) (h) (i) z 279 l MATHS ZONE 7

30 2 Find th valu of th angl in ach diagram blow. (a) (b) (c) b 108 c 114 (d) () 136 d (f) f Find th valu of th angl in ach of th following. (a) (b) (c) b b b c c b b c 60 c 4 Writ two xampls of thr angls that add to mak a rvolution. Worksht A5.5 5 Explain why adjacnt angls adding to 360 form a rvolution. Qustions Vrtically opposit angls Whn two lins intrsct, four angls ar formd. To answr th following qustion, click on th icon to th right to opn th Cabri Gomtry fils on ths angls. Obsrv what happns to th sizs of th angls whn you mov any of th points. You will nd to download Cabri Gomtry from th Maths Zon CD if you havn t alrady don so. What can you say about vrtically opposit angls? Explain why. You might want to rfr to supplmntary angls in your xplanation. Intractiv 5 angls 167

31 Whnvr two lins intrsct, four angls ar formd. In th following diagram ths angls d b hav bn lablld as, b, c and d. Pairs of c angls lik and c ar givn a spcial nam thy ar calld vrtically opposit angls. Thr is anothr pair of vrtically opposit angls in th diagram b and d. If you masurd and c with your protractor you would find thy wr th sam siz. Th sam is tru for b and d. Chck both of ths pairs of angls for yourslf. Vrtically opposit angls occur on ithr sid of th point whr two straight lins intrsct. Vrtically opposit angls ar qual. xrcis 5.7 Tutorial Vrtically opposit angls Prparation: Exs 5.5 and 5.6 Cor 1 Blow ar four pairs of vrtically opposit angls lablld with pronumrals. Masur th siz of th pairs of th vrtically opposit angls. (a) (b) You will nd a protractor. d c b b c d 168 MATHS ZONE 7

32 2 Find th valu of x in ach cas. (a) (b) (c) 33 x x x (d) () (f) 94 x x 89 x 12 Extnsion 3 Find th valu of th pronumrals in ach cas. (a) (b) 101 y z x z 88 x y (c) 31 x z y Worksht C5.9 Qustions Homwork 5.2 Worksht A5.6 5 angls 169

33 Summary Ky words Copy and complt th following summary of this chaptr using acut angl th words and phrass from th list. A word or phras may b complmnt usd mor than onc. complmntary 1 To masur an angl, th dot on th p must match up dgrs with th of th angl. Th lins must match up with obtus angl th arms of th angl. protractor 2 An angl of 40 has a of 50. rflx angl 3 angls add to 180. rvolution 4 angls ar qual. right angl 5 Th angl nams listd in ordr from largst to smallst ar straight angl r,,,, supplmnt and. supplmntary vrtx vrtically opposit Qustions 1 Us a dictionary to find th non-mathmatical manings of th words acut, obtus and rflx. (Don t writ ths dfinitions down.) Us ths dfinitions to xplain why ths nams ar givn to crtain angls. 2 Anothr word for rvolution is prigon. Guss what th prfix pri- mans, thn look it up in th dictionary. Find two words that start with pri and hav rlatd dfinitions. Writ thir manings. 3 If a rvolution is split into two angls and on of thm is rflx, what kind of angl is th othr? Is thr mor than on option? 4 A rvolution is dividd into thr qual angls. What kind of angls ar thy? 5 Explain th diffrnc btwn complmntary and supplmntary. 6 Unjumbl ths words: TMMLOPCEEN NTIORLUEVO ROTCTPRAOR 7 Writ th ky words from th list abov that hav part of th following words in thm: Worksht L5.1 flxibl rvolv supply comply Worksht L MATHS ZONE 7

34 FAQs I kp gtting confusd with which protractor scal to us (th insid or outsid on) whn masuring angls. How can I b sur I am using th right on? You nd to us th scal that starts at zro on th arm you ar masuring from. Also, you should always stimat th siz of th angl first. This is a way of chcking your answr. Is a 90 angl calld acut? No, a 90 angl is calld a right angl. An acut angl must b lss than 90. Is ABC th sam as CBA? Ys, ths angls ar th sam. Angls can b rad from ithr sid, but it is important that th lttr on th cornr of th angl gos in th middl of th angl nam. Cor 1 Us a protractor to masur ach of th following angls. (a) (b) hi.com.au 5.1 (c) (d) () (f) 5 angls 171

35 2 Draw an angl of ach siz statd. (a) 56 (b) 162 (c) 257 (d) Choos th corrct answr. M Which of th following is not tru of th angl shown? A It is namd NPM. B It is namd MNP. C It is approximatly 120. D It is an obtus angl. N 4 Choos th corrct answr. Which of th following is tru of th C angl shown? A It is obtus. B It is rflx. C It is lss than 180. D It is calld CFG. F P Stat th typ of ach angl blow (i.. acut tc.). (a) (b) (c) G 5.4 (d) () (f) 172 MATHS ZONE 7

36 6 Find th valu in ach of th following diagrams. (a) (b) (c) 66 (d) 55 7 Find th valu of th pronumral in ach cas. (a) (b) 5.6 x y y y Find th valu of th pronumral in ach cas. (a) (b) b 82 5 angls 173

37 Extnsion 9 Elois has constructd a mchanical lg to kick a football as part of hr physical ducation invstigation into kicking tchniqus. During on trial, th initial lg position was as shown. Find th siz of th rflx angl of th lg Building th Laning Towr of Pisa bgan in about th 12th cntury in Pisa, Italy. Evr sinc, it has gradually bn tipping sidways, and it would hav vntually falln ovr if nginrs and architcts hadn t found a way to stabilis th bas. (a) Masur th angl that th towr lans ovr from vrtical. (b) If it has bn falling for 800 yars, calculat th avrag angl it movs ach yar On th clock fac shown, what is th smallr angl mad at th cntr if th hands ar pointing at: (a) 12 and 2 (b) 12 and 7 (c) 2 and 7? , Writ th following Hindu Arabic numbrs as Roman numrals. (a) 12 (b) 49 (c) 368 (d) MATHS ZONE 7

38 2 Copy and complt th following magic squars. (a) (b) (c) Calculat: (a) (2 + 7) 6 (b) (c) 600 (5 (3 + 9)) 4 Find th nxt thr numbrs in ach pattrn. (a) 7, 4, 1,,, (b) 16, 8, 0,,, (c) 22, 12, 2,,, 5 Calculat: (a) (b) (c) Calculat: (a) 9 7 (b) (c) Writ th first four multipls of ach of th following. (a) 7 (b) 12 (c) 15 8 Which of th following numbrs ar divisibl by 9? (Us th corrct divisibility tst, not your calculator.) 108, 569, 4734, 9512, , Simplify: (a) (b) 2 6 (c) Copy and complt th following numbr pattrns. (a) 65, 56, 47,,, (b) 1, 4, 9,,, 11 Writ th following xprssions using pronumrals n for th IN numbr and m for th OUT numbr. (a) Multiply th IN numbr by two to gt th OUT numbr. (b) Add fiv to th IN numbr to gt th OUT numbr. (c) Subtract svn from th IN numbr thn divid by two to gt th OUT numbr. 12 If y = 2x 3, find th valu of y whn: (a) x = 0 (b) x = 4 (c) x = Assignmnt 5 5 angls 175