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Lesson 3 Problem Solving Practice Angles Of Triangles Answer Key Form Inquiry Instruction

all right students welcome back to this.Athenian stranger tutorial video where.today I thought it would help you with.some of the homework this is homework.two in the first problem we're asked to.find the missing angle and the thing.that I've asked you to do in addition to.simply finding the angle is indicating.what theorem or postulate that you used.to solve for the missing angle so in.this problem we're given a triangle and.we have two angles and we're missing the.third angle so we will use the triangle.angle sum theorem t AST.and what that triangle angle sum theorem.tells us is that if we add up all the.interior angles of a triangle they have.to add up to 180 degrees so the benefit.there is if we simply add 76 to 59 and.subtract that sum from 180 we'll have.the missing angle so I'm trying to find.a place to do that here 76 and 59.add up to see this is 15 carry the 1 7.plus 5 is 12 plus 1 is 13 so these add.up to 135 and if we subtract 135 from.180.we will get.answer that we're looking for so we have.to borrow here five from ten is five.three from seven is four so by the.triangle angle sum theorem this missing.angle is 45 degrees.now on to number two here we have an.exterior angle angle one and we have two.interior angles so what we're going to.use here is the exterior angle theorem.ei T and what that one tells us is that.the exterior angle of a triangle is.equal to the sum of the two non adjacent.interior angles so let me show you what.the adjacent angle is this would be the.adjacent angle and these two angles 62.and 67 degrees are non adjacent to angle.one so what we do is just add these two.together.62 plus 67.so 2 plus 7 is 9 and 6 plus 6 is 12 so.by the exterior angle theorem the.missing angle one is a hundred and.twenty-nine degrees that is the angle.that we found just now.we'll put here 129 degrees.now in this problem number three we're.presented with a unique situation first.notice that we're given the exterior.angle 152 and one non adjacent interior.angle so we can't we can't apply the.think about what the exterior angle.theorem is telling us.okay the exterior angle theorem is.telling us that this angle here is equal.to the sum of these two so what that.means is 152 degrees is equal to this.interior this non adjacent interior.interior angle 115 degrees plus the.unknown angle 1 which we'll call X so to.find X we just subtract 115 from both.sides.for the missing angle.to borrow for.I've turned it to for make two into a 12.v from 12 is 7 1 from 4 is 3.so the missing angle by the exterior.angle theorem is 37.because 37 plus 115 is 152 and that's.what the theorem tells us it would be so.this is 37 degrees.okay and number four.right away I'm noticing that angle 2 is.a vertical angle with angle 42 with the.angle that is 42 degrees that's opposite.so angle 2 is 42 degrees this is the.vertical angle theorem.angle 2 is 42 degrees.angle one can be found using the.triangle angle sum theorem angle 1 can.be found using the triangle angle sum.theorem which states that if we add 50.plus 42.we subtract that from 180 we'll find the.other angle because what the triangle.angle sum theorem says is that all the.interior angles of a triangle have to.add to 180 so first let's add fifty and.forty two together.ninety-two and we'll subtract 92 from.180.you.we have to borrow all the way over here.make this 17 in this 10 - from 10 is 8 9.from 17 is 8 so the missing angle is 88.degrees.so angle one is 88 degrees.angle 2 is 42 degrees now we just have.to find angle 3 which we can do using.the triangle angle sum theorem TAS T.we're given two of the interior angles.of a triangle 25 and 42 and we just have.to add them up 25 degrees and 42 degrees.you have to add those up 5 plus 2 is 7 2.plus 4 is 6 and we subtract 67 from 180.we have to borrow from the 8 turn into a.7 the 0 becomes a 10-7 from 10 is 3 and.6 from 7 is 1 we bring down this one so.the missing angle here at missing angle.3 is 113 degrees by the triangle angle.sum theorem.and number five we have a combination of.different triangles here.apply the exterior angle theorem to find.angle one you know we can't apply that.just yet because I noticed we're not.given angle two but what we can do is.apply the supplementary angles theorem.here 118 and angle 118 degrees in angle.one form a linear pair they are adjacent.to one another and if we have add these.together it has to equal 180 so angle 1.is just 180 minus 1 18.okay so angle one will be using the.supplementary angle theorem and if we.take 118 from 180 let's see what we get.first we have to borrow from the eight.turn it to a seven make the zero of 10.and now eight from 10 is two and one.from seven is six so by the.supplementary angle theorem angle one is.62 degrees.well now that we know that we can solve.for angle to angle two we can use the.triangle angle sum theorem because we.have these two angles inside this.triangle and all of these angles angle.to 62 degrees and 73 degrees have to add.to be 180 by the triangle angle sum.theorem so if I add 62.and 73.2 plus 3 is 5 6 plus 7 is 13.I get 135 so if I subtract 135 from 180.I will have the missing angle too so I.have to borrow from the a turn it to a.seven make the zero of 10 5 from 10 is 5.3 from 7 is 4 so this missing angle is.45 degrees this is 45 degrees so that's.angle 2 is 45 degrees by the triangle.angle sum theorem now we have to find.angle 3 and mmm there's a couple ways we.can do this.can see a couple different ways that we.could accomplish our goal.I think the most direct way would be to.imagine this as a larger triangle think.about it like this.this triangle here as a whole we have.this angle sixty-two degrees and we have.part of this angle part of its 45 and.this angle is 49 now they all have to.add up to 180 so what I'm suggesting.that we do is we add 45 62 and 49 and we.subtract that from 180 and that will.give us missing angle 3 so we already.did part of this didn't we I don't know.I guess we didn't so we need to add 45.and 62 together 45 and 62 and also angle.49 down here all three of these angles.have to be added together 5 plus 2 is 7.7 plus 9 is 16 carry the 1 4 plus 1 is 5.plus 6 is 11 plus 4 is 15 so these all.add to 156 so angle 3 will be 180 minus.156.by the triangle angle sum theorem.triangle angle sum theorem so let's.borrow from the eight make it a seven.make the zero at ten six from ten is for.five from seven is two so the missing.angle is twenty four degrees angle 3 is.24 degrees by the triangle angle sum.theorem.you.okay number six we have two parallel.lines indicated by these symbols here.these little arrows indicate their.parallel lines and I want to point out.that we have two different transversals.okay remember when we see a transversal.we're going to be thinking alternate.interior angles and here's that theorem.if you need a refresher if two parallel.lines are cut by a transversal then the.alternate interior angle angles are.equal so let's identify that the first.transversal there's two in the picture.here's one right here and what that.means is we have to look for the z shape.it can be a a regular z shape or it can.be a backward z shape in this case we've.got the regular z shape and what that.tells us remarkably I always find this.one remarkable is that angle three must.be equal to angle forty-seven by the.alternate interior angles theorem so.angle three is 47 degrees so angle three.by the alternate interior angles theorem.angle 3 is equivalent to angle 47.because they sit in the corner spaces of.that z shape.so angle three is 47 degrees.powerful tool the alternate interior.angles theorem now that we know that.angle three is 47 degrees.we noticed that angles three and four.form a linear pair they're adjacent to.one another which means they're.supplementary and have to add up to 180.so we subtract 47 from 180 and we'll get.angle 4 so let's do 180 minus 47.we have to borrow from the.eight make it a seven make the zero of.ten.seven from 10 is three four from seven.is also three and that one comes down so.angle 4 must be 133 by the supplementary.angles theorem supplementary angles.theorem SAT angle 4 is 133 degrees.how about angle 5 we do know enough.information to solve for angle 5 right.now.there's a.different ways you could do it we could.look at the transversal but we don't.really need to here's one thing we can.notice and this angle 52 degrees plus.angle five plus 47 if you take them all.together they would all have to add up.to 180 so what we could do is we could.add 52 and 47.see what we get there and then subtract.that from 180 to get angle 5 so 2 plus 7.is 9 5 plus 4 is 9 so I've got 99.degrees and if I subtract 99 from 180 we.do that over here run out of space.we'll take 180 and we'll subtract 99.okay we'll have to borrow all the way.over make this 17 make this 10 nine from.10 is 1 9 from 17 is 8.okay so the missing angle five is 81.degrees and that would be I guess by the.supplementary angle theorem.okay so angle five supplementary angle.theorem.angle 5 is 81 degrees.okay angle two we have two of the three.interior angles of this triangle shape.right here and so if we add up those two.interior angles that we have and.subtract from 180 by the triangle angle.sum theorem we'll be able to find the.answer.ta st for angle 2 and so I have to add.up 47 and 80 147 and 81.7 plus 1 is 8 and 4 plus 8 is 12 so I.got 128 if I subtract 128 from 180.I'll have it so I'm going to run out of.space here AC I'll do it here in this.little area 180 minus 128.let's borrow from the eight make it a.seven make the zero of 10 8 from 10 is 2.and 2 from 7 is 5 so this angle is 52.degrees angle 2 is 52 degrees by by the.triangle angle sum theorem angle 2 is 52.degrees now angle 1 let's take a look at.the other transversal here I'll.highlight it in green this transversal.right there now if you're looking for.the z shape.if you're looking for the z shape here.it is okay.right here see how that line into green.it's kind of a bent looking Z alright.this is what you need to understand this.angle one right here.is identical by the alternate interior.angles theorem to this entire angle.right here.okay so it's not angle five it's the sum.of angle five and 47 degrees so 81.degrees plus 47 degrees gives us this.missing angle 128 see we did the width I.already do the math right here 81 plus.47 so angle 1 by the alternate interior.angles theorem is 128 degrees.you.okay and if you didn't believe me on.that you could check by adding angle 1.to angle 2 they have to add to 180 so.let's check that 128 well look we did.the math here you see 180 128 and 52.angle 252 angle once 128 and they had to.they have to add up to 180 and they do.we show that by subtraction so these are.all correct and number 6.number seven I will leave you to do.because it's it's just a series of.things that we've already done you now.have enough information to do number.seven all on your own but they just take.too much time in this video.okay number eight we have to find the.value of x so here's what the algebra.creeps back in and I know that that.freaks people out and people start.losing their minds saying I don't know.what to do but just notice that you.could have called these angles one two.and three right they just happen they.just happen in this case to be algebraic.expressions but they still have to add.up to 180 degrees by the triangle angle.sum theorem right so that's all we're.really doing i what you need to do is.add them all together so let me show you.what that looks like.then after I pretty small so here all.right.ooh ten X minus 11.plus three X minus two.plus three X plus one.you.and all of that all of that.there has to add up to 180.okay.that's the key so now let's combine like.terms I've got two three X's there they.become 6x and I have a 10x so 6x plus.10x or 10x plus 3x plus 3x is 16x and.I've got here let me write that I've got.16x and then I've got a negative 11 and.a negative 2 those add together oh and a.positive 1 so let's do this negative 11.minus 2 is negative 13.plus one is negative 12 so this is minus.12 equals 180 so let's just add 12 to.both sides.you.sorry I'm being a little sloppy here and.trying to go fast.so we'll have to add here 0 plus 2 is 2.8 plus 1 is 9 and 1 so 16 x equals 192.we divide both sides by 16.now you won't have a calculator.available to you you know so.you know how do you divide this well.let's bring out a piece of scratch paper.and let me show you exactly how to do.192 over 16.okay now this might be a refresher for.some of you and for some of you it might.seem like a tedious bore but we're gonna.have to prime factor 192 and we're gonna.have to prime factor 16 that's the only.way we can do this because if you don't.know what 192 divided by 16 is you're.just going to be playing some game of.trying to figure out what multiplies.together to be what multiplies by 16 to.be 192 and there's a better way there's.a more clean way to do it.so let's just divide 192 by 2 okay so.we'll do this 192 and then this.weird-lookin division symbol here upside.down division so 2 goes into 19 nine.times with 1 remainder and 2 goes into.12 6 times with no remainder so 2 times.96 is 192 and we're just going to keep.dividing by 2 like this so 2 goes into 9.4 times with 1 remainder 2 goes into 16.8 times so we break it down again.96 breaks down into 2 times 48 and from.here we kind of can do it in our heads.right break it down again 2 times 24.break it down again 2 times 12 break it.down again.2 times 6 break it down again 2 times 3.so this is the full prime factorization.of 192 all these numbers around the.perimeter are prime.let's do 16 2 times 8 break it down 2.times 4 break it down.2 times 2 now what we're gonna do is.rewrite this fraction as product of.primes let me show it I mean.this is cool there's going to be a lot.of cool cancellations in this draw big.fraction bar and in the top you're going.to write all this one two three four.five six two's 2 2 2 2 2 2 6 2 s and 1 3.they're all multiplied together so this.is called the product of the primes and.then in the denominator we're going to.write the prime factorization of 16 2.times 2 times 2 times 2 and now we can.cancel out every time we've got a pair.of twos so here here you're here you're.here and here here so all that's left in.the numerator.two times 2 times 3 well 2 times 2 is 4.4 times 3 is 12 so 192 divided by 16 is.12 all without a calculator.so those 16s cancel and x equals 12 now.you're not done right you're not done.and you need scratch paper to do this.problem you now know that X is 12 so.what you have to do is you have to go in.and evaluate each of these little.algebraic expressions okay think about.it like this you have 10 X minus 11.okay if you put this into f of X.notation you could write f of X equals.10x minus 11 so evaluate.f of X evaluate the function at X equals.12.all right so this would equal 10 times.12 minus 11.okay so 10 times 12 is 120 minus 11 okay.that'd be 109 all right 120 minus 2 10.minus 1.yep 109 so this angle right here angle 1.is 109 degrees we just need to find one.more and then we can use the triangle.angle sum theorem to find the other.angle let's do this one so I'll say F of.12.equals three times 12.is one.okay well three times 12 is 36 plus one.is 37.see that so now I know this angle 2.right here equals 37 degrees well now I.don't have to do the other one I can let.me show you.so f of 12 equals 3 times 12 minus 2.okay so that's 36 minus 2 which is 34 so.this is 34 degrees but let me show you.how else you could have got it you could.have added 109 and 37 and subtracted.from 180 109.and 37.sixteen carry the one three plus one is.four bring down the one you got one.forty-six subtract that from 180.okay.this is a 10-6 from 10 is for 4 from 7.is 3 so you see it's 34 by the triangle.angle sum theorem so I wish they'd label.these angles I would say you should do.it like this the measure of angle 1.equals 109 degrees.the measure of angle 2 equals 37 degrees.and the measure of angle 3 equals 34.degrees and you did all that by the.triangle angle sum theorem ok and I.would put this in the box.I mean label the triangle by all means.but this is the way I would present it.it's easier to grade make sure you're.keeping your side work together I'm not.doing a very good job with the side work.here it's just kind of all over the.place ok let me show this on number 9.because number 9 is kind of weird we're.still going to be using the triangle.angle sum theorem but we're actually.given this angle that's 90 degrees.right that little symbol so what we can.say you you could you could look at you.could look at this two ways you know.that all the interior angles have to add.up to 180 right.so by this by this logic if you add 7x +.5 + 3 X - 5 + 90 it has to equal 180.all right so let me show that here.triangle angle sum theorem 7x plus 5.I'm sorry I'm left-handed plus 3x minus.5.Plus 90.as to equal 180.and a quick simplification would be to.subtract 90 from both sides.and now you only have to add up to equal.90 like that so let's see what we can.combine here these fives cancel out 5.and negative 5 and now I have 7 X and 3x.that's 10 x equals 90.this is easier than the other one isn't.it now we just divide both sides by 10.and you get x equals nine.so we can plug it in we can probably do.it on the paper here 3 times 9 minus 5.will give me this angle well 3 times 9.is 27 minus 5 is 22.this angle right here is 22 degrees and.now I can do 7 times 9 plus 5 well 7.times 9 63 plus 5 is 68.see 8 degrees right here.I guess we won't label I don't know I'm.getting lazy here I would just maybe.circle them there your angles here.and you did the triangle angle sum.theorem to get that okay number 10 you.have to apply the exterior angle theorem.remember the exterior angle theorem EA T.says that 151 is equal to the sum of the.two non adjacent interior angles so what.we can do is add these up and set them.equal to 151 so that's what I'm going to.write here 11 X minus 1 plus 20 X minus.3.fifty-one.and now you just have to simplify and.solve for X so let's do the common terms.here with the X's 11x plus 20x is 31 X.and negative 1 and negative 3 is.negative 4 and that equals 151 so now.we're going to add 4 to both sides.and 151 plus 4 is 155.so 31 x equals 155.and I can see right now that it's going.to be five because.you take 31 I mean I 31 times.five and then it's 15 so you divide both.sides by 31.just kind of did in my head x equals 155.well x equals sorry I got cocky there x.equals 5 so now we can plug in and solve.for the missing angles all right so.maybe you can almost do it in your head.at this point guys so 11 we're going to.plug in x equals 5 so 11 times 555 minus.1 is 54.five is 100 minus three is 97.okay.let's look at 11 what's going on.with eleven looks like I'm gonna have to.okay so we can this is by the exterior.angle theorem by the way eat same thing.here so we're going to set 14 X minus 3.equal to the sum of these two things.because this is the exterior angle and.these are the two non adjacent interior.angles so 14 X minus 13 is equal to the.sum of these two angles 4x plus 13 plus.6x plus 2.okay so combine like terms on the right.4x + 6 X or 10x + 13 + 2 or 15 so I've.got 10 X + 15 and we'll just bring all.this down 14x minus 13.and now we can just choose which side to.solve for Exxon get it Exxon like the.gas company.X 10 X on both sides and I get 4 X minus.13 equals 15 add 13 on both sides.and that adds up to 28 so 4x equals 28.so x equals 7 all right and now let's.just plug it in let's do the easy ones.first 4 times 7 is 28 plus 13 that would.be 28 38 41 okay so this is 41 6 times 7.here I'm doing this one 6 times 7 is 42.plus 2 is 44.and these added together are 85 and.that's what this should be all right I.just want to do it to make sure that.we're right 14 times 7.is 98 minus 13 let's make sure that that.comes up to 85 it does okay so this is.85.and these three angles were solved using.the exterior angle theorem.it's not that bad really what else is in.this thing find the values of x and y in.the diagram below okay so now we've got.x and y whoo all right.well we're given that this angle right.here is 6x minus 11 by the vertical.angle theorem these opposite angles are.equivalent so this is also 6x minus 11.and now we can use the triangle angle.sum theorem here alright to find out.what this angle is because we have.everything on this side in terms of x.over here we can't mix these two yet.because we have Y and X so let's solve.for the triangle on the right using the.triangle angle sum theorem what does.that mean well it means that 6x minus 11.X plus 5 plus 81.to be 180 that's by the triangle angle.sum theorem.okay all the interior angles of a.triangle have to add up to 180 so let's.combine like terms on the left.I've got 6x + x4 7x.and negative 11 and 5 gives me negative.6.+81 I guess I should have done that +81.just made myself an extra stub equals.180.I have to combine these two so 81 minus.6 is 75 so 7x plus 75 equals 180.tract 75 from both sides.7x equals 180 minus 75 which is 105.so let's divide both sides by seven and.let's hope that 7 goes into 105 evenly.otherwise we got ourselves a problem.okay it's going to because 7 goes into.10 once with 3 as a remainder and 7 goes.into 35 five times so it goes in 15.times X is 15 well now that we know X is.15 we can actually solve for these this.angle here and this angle here let's go.ahead and solve for this angle here 15.plus 5 is 20.so this angle is 20 and 6 times 15 what.is that.at 90 I can't remember so let's do 15.times 6.90 15 times six is 90 so six times 15 is.90 minus 11 is 79 so this angle here is.79.and this angle here is 79 by the.vertical angle theorem.well now that we know that we can solve.using the triangle angle sum theorem we.can do the same thing over here for y.because now we know that this is 79.let me if I'm gonna run out of space or.not I probably shouldn't have written.this here let me try to squeeze it in to.my one criticism in this packet there's.not enough space to do the work all.right 4y minus 18.plus y plus 14.equal 70 + 79.equals 180 that's the triangle angle sum.theorem at work again so let's combine.like terms I have 4y plus y is 5y.see if we can knock this math out.negative 18 plus 14 is negative 4.negative 4 plus 79 is 75 right so 5y.plus 75.equals 180 is that what I'm saying.tract 75 from both sides.and I have 5y equals 105 I know that.five is going to go evenly into that I.can do it in might we can do it in our.heads.five goes into 10 twice with no.remainder and 5 goes into 5 once so it's.21 times 5y equals 21 well now that I.know that y equals 21 I can just plug it.in here 21 plus 14 that's 21 31 35 so.this is 35 degrees and I can plug this.in here 4 times 21.is 84-84 -18.this is 66 let's see 84 74 64 plus 266.okay so this is 66.just double-check that 84 - 18.yeah 66 okay so this is 35 this is 66 79.79 81 and 20 solved all the angles.number thirteen okay so here you're.given a bunch of writing and it looks.hard and I don't like these problems any.more than you do so we just have some.triangle MNP and my advice Gaius is to.draw a triangle okay I don't know what.the angles are I'm just going to make it.up.it doesn't tell us anything about these.angles so just draw it draw it and you.know don't worry about what whether this.makes any sense visually so this angle.here M will label these m in P so angle.M.for X -3 angle in is 9 X -6 an angle P.is 6 X minus 1 so it wants us to find X.and the measure of each angle well.remember by the triangle angle sum.theorem all of these have to add up to.180 so let's just add 4 let me do it.correctly here 4 X minus 3.Plus.9x -.six plus 6x minus one.equals 180 combine like terms on the.left 4 X 9x + 6 X 4 X + 9 X is 13 X + 6.X is 19 X.19x and here i've got negative 3.negative 6 that's negative 9 minus 1 is.negative 10 make sure I did that right.4x plus 9x is 13 X plus 6x is 19 X okay.it just didn't it doesn't look right now.I got negative 3 negative 6 and negative.1 so it's negative 3 minus 6 is negative.9 minus 1 is negative 10 okay.10 X minus 10 equals 180.now we'll add 10 oh I see now we'll add.10 to both sides this is cool so 19 x.equals 190.divide both sides by 19 okay and X.equals 10.so now that we know X equals 10 we can.find all the other angles so 4 times 10.is 40 minus 3 is 37 9 times 10 is 90.minus 6 is 84.times 10 is 60 minus 1 is 59 and let's.check it to make sure we did it right.let's just add all these up and let's.make sure that they add up to 180 so 37.84 and 59 they should add up to 180 7.plus 4 is 11 Plus 9 is 20 carry the 2 2.plus 3 is 5 plus 8 is 13 plus 5 is 18.180 how about that so now we know that.angle M is 37.degrees we know that angle n is 84.degrees and we know that angle P is 59.degrees.okay number thirteen number fourteen.that's number thirteen done-for-you.number fourteen coming up in triangle.rst all right before we get in all that.nonsense we're going to draw a triangle.just to get a visual going.okay so this is triangle are s T the.measure measure of angle R is 5 more.than twice 6 so 2x plus 5 or sorry to 2x.plus 5.yep twice X is what I meant to say so.angle R is 2x plus 5.is angle s here one more than X so.that's X plus 1 and T is 16 less than 7.times X so 7 X minus 16.we're doing the same thing again guys.we're just gonna add all these up and.subtract from 180.I thought you know just I'll show you.something like another way to do this.you can stack add these two x + 5 X + 1.+ 7 X - 16 okay they can be added and I.don't know if you'll find this easier or.harder but you kind of add them you kind.of add them like like they're two.separate things so 2 X plus X is 3 X + 7.X is 10 X and then 5 plus 1 is 6 - 16.six minus 16 is negative ten so that's.ten X minus ten okay and all that has to.equal 180.all right so you add 10 to both sides.now you have 10 x equals 190.divide both sides by 10 so X would equal.19 okay and if that was confusing to you.show it another way you would just do 2.X plus 5 plus X plus 1 plus 7 X minus 16.equals 180 all right so this is the way.we were doing it before you're just.doing the same thing 2 X plus X plus 7 X.2 X plus X is 3 X plus 7 X is 10 X.five plus one is six minus 16 is.negative ten so you're just back to.where you were before it's your.preference whether you like the stack.adding method or not can be confusing so.now we know that X is 19.the math harder okay so two times 19 is.38.plus five is 43 so this is 43 19 plus 1.is 27 times 19 minus 16 well I actually.don't know that one right what's 7 times.19 you know what we could do is just add.43 and 20 and subtract from 180 so 43.plus 20 is 63 and let's do 180 minus 63.then we'll check our work this is 7 and.10 so 7 1 1 117 okay so let's check that.let's see if 7 let's see if 19 times 7.minus 16 is 117.okay so this is 63 carry the 6 oops why.order 3 and then it's 13 136 minus 16.you.okay oh no that's not gonna work mmm oh.I don't know why I wrote I got it all.backwards I must be getting tired it is.9:52 p.m. so 9 times 7 is 63 and I wrote.a 6 I just did it again.9 times 7 is 63.carry the 6 1 times 7 is 7 plus 6 is 13.so now I have to subtract 16 from 133.okay so now I'm going to borrow the 2.and make this 13 and here we go so 13.minus 6 is 7 2 minus 1 is 1 and 1 so.yeah it checks out.this is 117 so this is 43 this is 20 and.this is 117 so R is 43 I suppose we.should check it right well we kind of.did 43 plus 20 plus 117 does add up to.180 s is 20 and T is 117.okay I think you can do I think you can.do numbers 15 and 16 on your own because.this is 51 minutes long already.so really if you've watched this video.you have to do all by yourself number.seven number 15 and number 16 you should.be able to do that guys listen I put.myself out there tonight doing this I've.recorded like two and a half hours of.videos tonight.just for geometry if you found this.helpful if this benefited you if you.think this will help your grade and help.your understanding please consider.giving the video a like and leaving a.comment the comments are what's going to.propel the video in the search rank so I.would love for you to leave comments and.like this video and if you haven't.already if you're a student in this.school even if I'm not your teacher but.you're watching this video please.consider subscribing and hitting that.little notification bell so you're.always alerted to when I release new.videos because not all of you are on the.remind group so you're not getting these.messages alright guys thank you very.much have a great day.

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Lesson 3 Problem Solving Practice Angles Of Triangles Answer Key Form FAQs

Some of the confused FAQs related to the Lesson 3 Problem Solving Practice Angles Of Triangles Answer Key Form are:

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How do I write pseudo code for this: "input 3 side of a triangle and figure out if its scalene, isosceles, equilateral or right angle triangle?

Input three side lengths a,b,c. a,b,c. If a=b a=b and b=c b=c this is equilateral else if a=b a=b or b=c b=c or a=c a=c this is isosceles. else this is scalene. If a 2 + b 2 = c 2 a2+b2=c2 or a 2 + c 2 = b 2 a2+c2=b2 or b 2 + c 2 = a 2 b2+c2=a2 this is a right triangle. Both isosceles and scalene triangles can be right triangles.

How do I create a fillable HTML form online that can be downloaded as a PDF? I have made a framework for problem solving and would like to give people access to an online unfilled form that can be filled out and downloaded filled out.

If it's a single-page form, the unprofessional way to download the filled form as PDF is to print on chrome and firefox browsers and save as PDF or you can implement a simple button that does the same thing or download a section of the page if you don't want a section of the page to be downloaded along with the PDF. On the other hand, the best way to handle this is to use a web-based Form builder like Formplus. Formplus is an online and offline data collection tool that allows you to create and customize your forms to your taste. You or/and respondents can get notifications of the filled form as PDF or docx.

The perimeter of a right angled triangle is 72 cm, and the lengths of its sides are in the ratio 3:4:5. How do you work out the area?

Is this a homework question? Here is the answer. assume of three sides are 3a, 4a and 5a Sum of all sides is 72 = 3a+4a+5a = 12a From step 2, a=6 Sides are 18, 24 and 30 Area = 18 x 24/2 = 216 Next time try doing your homework yourself.

How do you solve a mathematical question if you are given all the sides of a triangle and you are asked to look for one angle?

You can use the cosine rule for a triangle. cos(A) = (b^2 + c^2 - a^2)/2bc Similarly for, cos(B) = (a^2 + c^2 - b^2)/2ac cos(C) = (b^2 + a^2 - c^2)/2ab

How does one formulaically determine the precise angle to bend the four sides of a given sheet metal pyramid? I have worked this out using projection drawings and trigonometry, but wonder if anyone has one formula to solve a variety of dimensions?

I assume that you have in mind a pyramid with a square base and four identical triangular sides that rise symmetrically to a common vertex located directly above the center of the base. With apologies for the poor artwork, let H H and W W be the pyramid’s height and base width, respectively, and let θ θ be the angle of inclination of the sides relative to the base: Then  cosθ= W/2 (W/2 ) 2 + H 2 √ ,   cos⁡θ=W/2(W/2)2+H2,  so that the angle itself is the inverse cosine of that quantity:  θ=arccos( 1 1+4( H 2 / W 2 ) √ )   θ=arccos⁡(11+4(H2/W2))  (Editing to add the computation of a different angle - the one between neighboring sides) You can express the angle between neighboring sides as the angle between the normal (perpendicular) vectors to the respective sides. Consider a coordinate system in which the axes point in the following directions: 1) out from the center of the base of the pyramid to the midpoint of the bottom of the first side of interest; 2) vertically, from the center of the base up through the vertex; 3) out from the center of the base to the midpoint of the second side of interest. A normal vector to the first side can be written as (H,W/2,0) (H,W/2,0) , and a normal vector to the second side as (0,W/2,H) (0,W/2,H) . If \alpha is the angle between these vectors, then:  cosα= (H,W/2,0)⋅(H,W/2,0) |(H,W/2,0)||(H,W/2,0)| ,   cos⁡α=(H,W/2,0)⋅(H,W/2,0)|(H,W/2,0)||(H,W/2,0)|,  so that the angle between the sides is:  α=arccos( 1 1+ 4 H 2 W 2 )   α=arccos⁡(11+4H2W2) 

Is it good practice to watch YouTube videos and Khan Academy to learn how to solve problems in engineering school, instead of figuring them out yourself?

It is great to watch videos to understand how to do something, but you won’t know that you really understand until you practice the problems without any help. Feel free to watch those videos to help you better understand a topic, but to be truly confident in your fluency of a topic, practice will make perfect :)

How can we solve this question? A square of a side x cm has the same area as a rectangle of length (3x+5) cm and width (2x-3). How can you form an equation in x? How can you show that it simplifies to 5x+x-15?

How can we solve this question? A square of a side x cm has the same area as a rectangle of length (3x+5) cm and width (2x-3). How can you form an equation in x? How can you show that it simplifies to 5x+x-15? Q1: What is the area of a square? A1: The length of its side squared So, the area of the square in your question (in square centimetres) = x 2 =x2 Q2: What is the area of a rectangle? A2: The length of its long side multiplied by the length of its short side. So, the area of the rectangle in your question (in square centimetres) =(3x+5)(2x−3)=6 x 2 +x−15 =(3x+5)(2x−3)=6x2+x−15 From the question, we are told that Continue Reading

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