Calculating Angles in Geometry 7 5 14

hello welcome back the title of this lesson is called calculating angles this is part one so in this lesson we'll have series of geometric diagrams and we'll give you some information in the drawing and we'll have to calculate the numeric value of an angle now i'll tell you right now that all of these problems really only require addition and subtraction to solve them so they'll be very easy for you just to subtract and add no problem but we're going to write down the solutions kind of as an equation and use an equation to solve it even though you could just skip ahead to just straight subtraction because want you to practice your equation skills so when you look at these you might say could could just do this that's fine but also want you to get practice solving equations so here's our first our first question we have this diagram here we have two kind of lines that go on and forever and ever in both directions so we have this angle here of 120 and we're trying to find the angle now remember we learned about vertical angles anytime you have an or plus the opposite angles there on either side are equal so these angles are actually equal to each other so without doing any math at all you know that the angle has to be 120 degrees there's nothing to add or subtract because you know they're equal and just as an aside these angles here are also the same you can see that they look to be about the same as well so opposite angles in situation like this we call them vertical and so we know the answer is 120 without any further work all right let's take look at problem number two we have this situation it's very similar in fact it's the same drawing except now we have angle over here and we're trying to figure out what is the angle now you need to start getting in the habit of seeing when you see these straight lines that are broken up by another segment or line these are what we call supplementary to each other they add up to 180 degrees and you know this because any angle on straight line from one side to the other has to be 180 degrees so this plus this has to be 180 so in equation form what you would say is 120 plus whatever is in degrees has to equal 180 degrees this is what it means to be supplementary now in order to solve this we'll just kind of spread it out little bit and ask ourselves how do we get by itself well we have positive 120 so we'll subtract 120 from the left and subtract 120 from the right and on the left of course the 120 minus 120 is zero so all we have left is and 180 minus 20 is 60 degrees so just put 60 and the the unit is degrees so 60 degrees so this is what what was saying minute ago you can just solve these with subtraction you know that this has to be large angle of 180. subtract this away minus the 120 has to be what you have left so you can do that but am writing them in terms of equations and subtracting from both sides because want you to get practice with with this kind of procedure with equations all right so 60 degrees that was the answer there let's take look at problem number three what is the measure of angle here now first you're not really sure what to do because is way off by itself and you don't really know anything about what's going on over here but you need to learn how to read geometric diagrams when you see like an angle marking here and then there's like another angle marking there and if it's true geometric diagram it's like you know congruency marks when you want to tell you when you want to tell me that the length of the sides are the same you put little mark on the sides well for angles if you put little mark here or little angle arc and it matches the angle mark here then you can assume those to be equal if it's proper geometric drawing right in this case so what you know is that this is 134 degrees but even though it's not written there you know that this is also degrees so then how do you find well this must be total of 180. so what you say is whatever it is plus 134 must equal 180 because this plus this must then be 180 so then you just solve it so plus 134 equals 180 and then we'll just subtract 134 subtract 134 and what we will get on the left is because this just disappears is going to be equal to 46. degrees circle that so 46 degrees and you can check it by putting 46 back in here the six and the four would make bring it up to 140 and the 140 plus the additional 40 is 180 so that is the correct answer let me take these now we have few more problems in this lesson all right here is problem number four we have this kind of rectangle here but we have rectangle where corner to corner it is sliced in half here and we're trying to find angle so on the diagram that is this angle measure from this segment here over to this one so this is angle if you need to visualize it you can kind of draw little arc like that that's angle now what do we do we know that these corners here these little squares indicate 90 degree angles so up here what it means is 32 degrees plus whatever happens to be must be equal to 90. so these are complementary angles remember supplementary means they add to 180 but complementary means they add to 90 and these have to add to 90. so we say 32 plus whatever is has to be 90 degrees all right so we write it 32 plus is 90. now in order to get by itself we'll subtract 32 from the left we'll subtract 32 from the right and this will be zero so we'll just have by itself what is 90 minus 32 that is 58 degrees and you can check it by putting 58 back in here and adding it to 32. if you add put 58 the 2 will make 60 and then 70 80 90 and so that makes sense so the answer is 58 degrees for 58 degrees all right let's take look at problem number five what is the measure of angle right so this angle from this ray down here well we know that this from this side of line all the way to the other side must be 180 so these are supplementary angles they add to 180. so 109 right plus whatever is has to be the same as 180 right but we want to get by itself so we subtract 109 subtract 109 and the only thing you'll have left is because this goes to 0 and then what is 180 minus 109 you get an answer of 71 degrees so 71 degrees check yourself if you put 71 in here and add to 109 the 1 will make 110 and then 70 more will make 180 and you know the whole thing has to be 180 degrees this is actually why we learned about complementary and supplementary angles because it helps to solve problems because we geometrically know it has to add to 180 and so we have we define those terms for that reason all right let's take look at this problem what is angle that is this angle right here between the rays now maybe little hard to see you may have to turn your head sideways but this is line and the angle that goes from this side all the way to the other side again has to be 180 so when you add this angle plus this angle it must be 180. 143 plus whatever is has to be 180 so 143 just spread it out so have little room how do get by itself i'm just going to subtract 143 subtract 1 43 all have left on the left is because this goes to 0 and what is 180 minus 143 37 degrees so 37 degrees you can check it by putting it back in here the 7 going in here will make 150 and then 160 70 80 with 30 more and that's the final answer all right here is number seven now this is what where it starts to get little more useful to write things as an equation because you're trying to find angle but this looks like totally different situation than what we have covered before we have lots of situations where we've had just line and it's cut in one place and we know they add to 180 so at first you look at this and you're not totally sure what to do until you realize that this must all be 180 degrees so this angle plus whatever it is plus 73 all of them together must equal 180 so 68 plus whatever is plus 73 must all together add up to 180 degrees all right now when you add 78 and 60 sorry 68 and 73 together you're going to get 141. right so how do we solve for just spread it out and can do what want to both sides so i'm going to subtract 141. 141 from the left 141 from the right so it disappears here so is going to be equal to 180 minus 141 39 degrees so 39 degrees and you can check yourself because we just figured out that these two together when we add them together comes out to 141 so if you put 39 in there and add it to this it'll be the 9 will go in and make 150 and then 160 70 80 180 when you add that 30 more so it's 39 degrees let me take this one down we have one more and call it day okay here's our very last problem we're asked to find the measure of angle but it looks little weird because on this side over here we don't really have any other numbers but what we have figured out is that there's couple of different ways to tackle this right first of all you notice that this is 90 degrees right so the whole thing is 90 degrees because of the square right here so we could find if we only knew what this angle was but it's not really written here but then we realize wait minute it has an angle marking and over here has another angle marking so because this angle marking matches this one we know that this angle is the same as this angle in fact it looks to be about the same doesn't it so actually this 41 degrees is the same as this one down here 41 degrees and you know that because of the angle marking here right now that you know that this is 141 degrees you can write down that 41 degrees plus whatever is has to equal what 90 because this is 90 degree angle so we'll just solve that equation how do we do it well let's just subtract 41. this gives you zero so all you have is 90 minus 41 comes out to be 49 degrees 49 degrees and double check yourself you put 49 in here and you add one more that'll be 50 and then the 50 plus the 40 left over is the 90 and so you verified that it is 49 degrees so this lesson was kind of you know it's kind of an all around measuring angle calculating angle kind of lesson you know it's kind of hodgepodge of lots of different things basically what we have is situations where we draw figures and ask you to calculate the angle and as said at the beginning you can solve all of these by addition and subtraction if you look back through all of them they're all solved by taking 180 minus or 90 minus and you can do it that way but like to write the equations down especially now that we've done it so much so that you can practice writing equations now because this kind of thing you'll be surprised when we get into classes down the road in physics where the problem is easy to solve but the student can't get there because they don't know how to write an equation down so we have to start with simple situations where you know this plus this has to equal 90 and solve it and this plus this has to equal 180 and solve it because later on when we're in physics and we have motion of ball and force then we have to write an equation this plus this has to equal this and that skill of looking at situation drawing that you sketch or that give you and writing down an equation is just as important as learning how to solve the equations so even though these seem simple do want you to solve them by writing an equation you're going to have to trust me that that skill will serve you well going down the road in your future studies so practice these we have more like this in part two so follow me on we'll conquer it right now