t9t suaroaql ulns-albuv uo6^lod aql S-€ uossal

uo3-00l 'SZ uo3-8l'tZ uo3€cepop'€Z uo?etued 'ZZ

'uo8{lod.ruPEar

qJBa Jo a13uu rogage uB puu alEuu logalul uB Jo sarnsuelu aql pulll

uo3-7991'91

uo8ecep'91

uo3-97'V1

uo8ecepoP'71

'9r

erqably ffi

(Ogl abed)

5 a;duex3

(Ogl abed)

tr a;duex1

(6st a6ed)g alduexl

(991 ebed)

7 alduex3

Y/ [:i1A . n l r y

(>, 'l'Jl@

-\q "1'l/

\ /\!{----lg 'oz

------t\

[

.'/

Wgl-:alll 'Lr'sernsualu a13uu Sulsqru eql Pu!f,

.uo8,{1od qrua Jo sa18uu eql Jo salnsueru eIIl Jo rrns aql puld

'aagtuot Jo xeauot s1 uo3't1od aql Jallleqa IIoI

'sepls Jo raqlunu s11 .{q uo3't1od aql '{31sse13 'qdul8o1oqd qrua ul uo8'{1od B pul'{

N s tO//1/ \ H t d / \

I )" '\-----------7 - t \

- . t / \ / ^ ( ) *v \ / \ / v '\__---/ar d 'L )----------) '9 I I 's

'se13uu puu sepls s11 ,{;puep1 uaql'saJpral s1r '{q uo8'fiod qcua arrruN

(lSl a6ed)

1alduex3

',{q,l.r ga1 'lou JI ;uoE,t1od u arn8g eql s1 a;dtuexg [q al;Per4 G)

4 " .9€ l

O

'il!45 e4X1 aos 'sas!)loxa oloul lol ffi

Packaging The nut container at the right has theshape of a regular octagon. It fits in a square box.A cheese wedge fills each corner of the box.

26. Find the measure of each angle of a cheese wedge.

27. Crit ical Thinking Show how to reaffangethe four pieces of cheese to make a regularpolygon. What is the measure of each angleof the polygon?

IJse a protractor. Sketch each type ofregular polygon.

Sample: dodecagon

Use the protractor to equally space 12 pointsaround a circle. (360" + 12 : 30",so mark a pointevery 30".) Connect these points to form a Iregular dodecagon.

@ opplv Your Skills

Connection

At a theater-in-the-round,seats are arranged so theaudience surrounds the staoe.

28. triangle

30. hexagon

(A) 25(F) s0

29. quadrilateral

31. octagon

a_e ) 115a-D) 160

The sum of the measures of the angles of a polygon with n sides is given. Find n.

3 2 . 1 8 0 33. 1080 34.1980 35. 2880

36. Multiple Choice In the figure at right, LB = LD andm L C : 1 3 0 . W h a t i s m L B ?

Hornework Video Tutor r@---

Visit : PHSchool.comWeb Code: bce-0305

162 chapter 3

37. Stage Design The diagram at the right shows platformsconstructed for a theater-in-the-round stage. Describe theIargest platform by the type of regular polygon it suggests.Find the measure of each numbered angle.

38. Error Analysis Miles said that he measured an angleof a regular polygon to be 130'. Explain why this resultis impossible.

39. Critical Thinking A triangle has two congruent angles and an exterior angle witlmeasure 100. Find two possible sets of measures for the angles of the triangle.

The measure of an exterior angle of a regular polygon is given. Find the measure oan interior angle, and find the number of sides.

40.72 41.36 42.78 43.30 44. x

45. Probability Find the probability that the measure of an angle of a regularru-gon is a positive integer if n is an integer and 3 < n -< 72.

ffi nO. Algebra A polygon has n sides. An interior angle of the polygon andan adjacent exterior angle form a straight angle.a. What is the sum of the measures of the n straight angles?b. What is the sum of the measures of the n interior angles?c. Using your answers above, what is the sum of the measures

ofthe n exterior angles?d. What theorem do the steos above lead to?

Paral le l and Perpendicular L ines

I

€9r soro-e)q:apo) qaM'ruo)'toor.psHd :ltst^ zlnb uossal aulluQr <htseprs luenJduoc eeJql qlla\.zg

seprs IuJJB[peluenJSuoJ Jo sJr€d o^\l qlr^\ '09

€t tz-q)q :apo) qa^sal noa)olo

roleln)le) 6urqdelg :ro1lll0sloollcslld-------_-)

euHu(F oDr

' roleln)le) 6urqdel6 rno,{

seprs luenJduoc JnoJ Hll.rn 'gn

soprs alrsoddoluenJSuoc 1o srred ol$ q1I.4A 'I9

'upldxa'a1q1ssod lou JI'peqlrJsep lurolellrpunb a,ruruor aq1 6e1q1ssod g smurq

'sfur Surlcesrelureql dq poruJoJ se13ue alno€ aql Jo ernsueu eql pulC'JoIJeluI s,uo8ecep eql

ur lJesJelur pue uo8ecep reln8er u;o seySue elrlncesuoJ oA\1 lceslq s.{er o.tta '69

suo8flod eqt ot suedduqleq.{\ osle uruldxg'Jeqrunu e8rel e seuoceq u se suoS-u relnSar;o se13ueeql ur seJnseeu eql o1 sueddeq leqr*r urc1dxa ol eFruJoJ puoJes eq] esn 'q

'fr - osr puu (zr+)o8r sernruroJeq1 dq ue,rt8 sr uo8-a relnSer u;o e13ue ue Jo eJnseeu eql fq.l ureydxE 'u 'gg

'ureldxg e.08T Jo e13ue ue qlpr uo3-u rep8er € eJeql sI 'p'uo3-ggg1 rep8er u;o e13uu ue Jo eJnsEaIIr eql

lnoqe lueruelets € e{eru'(q) ued ruoryqderS eql uo pes€g slsf;euy e]eq 'r

'lq8tr aql le u^\oqs auo eql oIII,ropur.r e Sursn srrcd perepro eql lold 'q

'(apue qcee JoeJnseoru'u) uro; eq1 ur srmd peJepJo

se qluel lsaJeeu aql ol sllnsa: .rno,{pJocaU '002 ' ' ' ' ' 08 ' 09 '0V '02 : u

roy uo3-u repSer e ;o e13ue ue;o' r (J l uUo-u ' tu l t ro3J u JU dlouu uu JU Harns€eu aql purj roteln)le) 6urqde.r9 'E 'rs

ffi e6ualleq1 6|

7 = l)sA 0Z = l)sxt8l = xeu^ 002 = xeLux0 9 l = u l u l ^ 0 = u l t u x

uo rotd rvls pue M] esn'sred pe.rapro eq1 qdet6 o1

'uorlrpuo) puo)os aq+leeur o1 1r lsnfpe uaql

'uorlrpuo) lsjrl aq+laeuJ ol elnbr; e qr1e1s

'€s-ls sosr)raxl ul

ulH ou!^los uaHord

iuo8,(1od oql Jo erueu eql sI 1€I{l11'uo3.{1od etues eql yo a13ue rolrelxe ue JoeJns€eru eql setuq eeJql sr uo8,{yod reln8er e;o e13ue JoIJeluI ue Jo oJnseelu eql '9S

'lqdrJ eql lBern8g eql lnoq€ ,rou>I no.{ leqm ileI 6uttl,r6 'SS

'ureldxg e{Jo^\ poqteru

req seoc'09€ slserlqns ueql pue'0BT ,iqsaldrlpur'se18uerr1 Jo Joqrunu eq1 slunoc

'xe1Je.t qcee ol lueruSes e sa€Jp'uo3,{yod eqleprsur lurod e s>1crd eqg'uo3,(1od e;o sepue

aql Jo serns€eru eql Jo Iuns oql puu o1 .{emreqtou€ s€q aqs sdes uelE 6ul4ulql lp)tty)

'tS

prelepnbe lou sI leql uo3,{1od reln8uetnbe uB '€S

relnSuernbe lou sI l€ql uo3,{yod leralepnbe uv 'Zg

rupSar lou sr leql leralelrpenb relnSuernbe ue 'IS

ruln8uembe 1ou sr 1Bq1 preleprpenb e 'gg

'tS-09 saslrraxf, uI peqlrrsep arn8g qrua qrle{S papul-uado

-\\Y

$ $

'LV'8?'6n

'uo8.{1od aql erueu ueqJ'arnsuaru alEuu Eqsspu qrua puld elqeFly ffi