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NAME:___________________________ Math8,Period1and2 Mr.Rogove Date:__________ Learning Objective:Wewillsolvewrittenlinearequationsthatinvolve findingmissinganglemeasures.(G8M4L4a8) Concept Development: Whenyouaretryingtowriteandsolveanequation(especiallywherethese geometryquestionsareconcerned),itcanbehelpfultoDRAWAPICTURE. Example:Inarighttriangle,thefirstangleis22morethan3timesthesecondangle, andthethirdangleistherightangle.Whatarethemeasurementsoftheangles? DrawaPicture: Solution:Letxbethesecondangle. Reminders: 1.TwoanglesthatareCONGRUENTareequalinmeasuretoeachother 2.IftwoanglesareSUPPLEMENTARY,theyaddupto180degrees. 3.IftwoanglesareCOMPLEMENTARY,theyaddupto90degrees. 1 G8M4L4a:WritingandSolvingEquationsInvolvingAngleMeasures NAME:___________________________ Math8,Period1and2 Mr.Rogove Date:__________ Guided Practice: StepsforSolvingforMissingAngleMeasures 1.Readtheproblemcarefullyanddefineyourvariable. 2.Ifhelpful,drawadiagram. 3.Writeanequationusingvariables. 4.Ifnecessary,usethepropertiesofequalitytogetallofyourvariablesononeside oftheequation. 5.Combineliketerms. 6.Usethepropertiesofequalitytoisolateyourvariable. 7.Interpretyouranswer. Apairofcongruentanglesaredescribed Oneanglemeasuresninemorethansix asfollows:themeasureofoneangleis timesanumber.Ananglecongruentto threemorethantwiceanumberandthe thatoneisdescribedasbeingthirtyless otherangle’smeasureis54lessthan thanninetimesthenumber.Findthe threetimesthenumber.Findbothangle anglemeasures. measures. Themeasureofoneangleisdescribedas Oneangleisonelessthansixtimesthe twelvemorethanfourtimesanumber. sizeofanother.Thetwoanglesare Itssupplementistwiceaslarge.Findthe complementaryangles.Findthesizeof measureofeachangle. eachangle. 2 G8M4L4a:WritingandSolvingEquationsInvolvingAngleMeasures NAME:___________________________ Math8,Period1and2 Mr.Rogove Date:__________ Atrianglehasanglesdescribedas follows:thefirstangleisfourmorethan seventimesanumber.Anotherangleis fourlessthanthefirst,andthethird angleistwiceaslargeasthefirst.Find theanglemeasures. Arighttriangleisdescribedashavingan angleofthesize“sixlessthannegative twotimesanumber.”Anotheranglewas “threelessthannegativeone-fourththe number”andthethirdanglewasaright angle.Findthemeasureoftheangles. 3 Oneangleofatriangleis3lessthanten timesanumber.Thesecondangleis32 morethantwicethenumber,andthe thirdangleis17lessthantwelvetimes thenumber.Findtheanglemeasures. Oneacuteangleofarighttriangleis describedas9morethanthreetimesa number,andtheotheracuteangleis10 lessthan4timesthesamenumber. Whataretheanglemeasures? G8M4L4a:WritingandSolvingEquationsInvolvingAngleMeasures NAME:___________________________ Math8,Period1and2 Mr.Rogove Date:__________ Independent Practice: Themeasureofoneangleisthirteenless thanfivetimesthemeasureofanother angle.Thesumofthemeasuresofthe twoanglesis140degrees.Whatisthe measureofeachangle? Theanglesofatrianglearedescribedas follows:∠!isthelargestangle,its measureistwicethemeasureof∠!.The measureof∠!istwolessthanhalfthe measureof∠!.Findthethreeangle measures. 4 Ananglemeasureisseventeenmore thanthreetimesanumber.Its supplementisthreemorethanseven timesthenumber.Whatisthemeasure ofeachangle? Themeasureofoneangleiselevenmore thanfourtimesanumber.Asecond angleistwicethatsize.Thesumoftheir measureis195degrees.Whatisthe measureofeachangle? G8M4L4a:WritingandSolvingEquationsInvolvingAngleMeasures NAME:___________________________ Math8,Period1and2 Mr.Rogove Date:__________ Threeanglesaredescribedasfollows: ∠!ishalfthesizeof∠!.Themeasure of∠!isequaltoonelessthantwo timesthemeasureof∠!.Thesumof ∠!and∠!is!!"°.Cantheseangles formatriangle?Whyorwhynot? Twointersectinglinescreatedfour angles.Oneanglemeasureis220more thaneighttimesanumber.Itsvertical angleis181morethanfivetimesthat samenumber.Findtheanglemeasures. 5 Apairofverticalanglesaredescribedas follows.Oneangleisfourtimesa number,andtheotherangleisforty-five lessthanninetimesthatnumber.What isthemeasureofeachangle? Twointersectinglinescreatedfour angles.Oneanglemeasurefifty-seven morethanthreetimesanumber.An adjacentangleistwenty-onelessthan fivetimesthenumber.Whatarethe anglemeasures? G8M4L4a:WritingandSolvingEquationsInvolvingAngleMeasures NAME:___________________________ Math8,Period1and2 Mr.Rogove Date:__________ Activating Prior Knowledge: Wealreadyknowaboutcomplementaryandsupplementaryangles. Ifoneangleis75degrees,whatisthe Ifoneangleis31degrees,whatisthe measureofthecomplementaryangle? measureofthesupplementaryangle? Closure: Apairofcorrespondinganglesaredescribedasfollows: themeasureofoneangleisfivelessthanseventimesa numberandthemeasureoftheotherangleiseight morethanseventimesthenumber.Aretheseangles congruent?Whyorwhynot? Teacher Notes: ENYLesson5 KhanHW:EquationPracticewithAngleAddition 6 G8M4L4a:WritingandSolvingEquationsInvolvingAngleMeasures
