 But here, let me give you the formula for this. Take a look at this thing, and then we'll get into the vectors, okay? Slick make, take a look at this thing, a triangle Okay, doesn't make a difference. What type of triangle? The sum of the angles in a triangle are 180 degrees So this angle plus that angle plus that angle sum of Angles in a triangle is equal to 180 degrees Okay, that's the sum of the angles in a triangle. I need to start killing pens I'm gonna start killing pens gang. Let me know if this is not coming out bright enough for you Okay, I was gonna go get some pens, but I didn't get a chance to do it. Okay It's like my Odyssey channel, it's like my Odyssey channel. It's like a 69 Your device is always taking deeply wrong take so some of the angles in triangles 180 degrees, right now if these sides are The same equal then each one is x x x which means all the angles are the same Right, so let's kill the x here if all the sides are the same then all the angles are x x x Right because all the angles control the size, right? So basically x plus x plus x has to equal 180 degrees because they're all the same So three x is equal to 180 degrees a divide by three. So x is equal to 60 degrees, right? Now here's a four-sided shape and we'll go up to five sided shape and I'll give it a low down on this, right? So whenever you want to find the sum of the angles in any polygon break it down into triangles, right? So a four-sided Polygon if you break it into two triangles from one point you break it into triangles then this triangle this these angles added up or 180 and these angles added up or 180. So the sum of the angles in a Quadrilaterals of four-sided triangle is 360 degrees because it's two triangles so two times 180, right? What the hell is this? Complicated. Eighth grade. You're gonna do this by the way. You end up doing this in grade grade nine, okay Pay attention here. You'll see it all of a sudden. I'll just click and you go. Ah, this is simple, right? Like you have two triangles here one triangle two triangle What's the sum of the angles in this triangle? 180 degrees. What's the sum of the angles in this triangle? 180 degrees. What's 180 plus 180? 360, right? So the sum of the angles, sum Angles in a quadrilateral in this, I'm just gonna say in this is equal to two times 180 degrees which is equal to 360 degrees. Okay Makes sense. Okay. Okay done deal. Watch this seriously. You're gonna this comes up to you in grade Maybe even grade eight, right? Now, let's try a five-sided and then we're gonna come up with the equation for this. So five-sided polygon Now it doesn't have to be a regular polygon. Remember, regular regular polygon means all sides are equal They're all the same length, right? So let's assume they are there. We don't care if they are where they are right now, right? So we want to right now figure out what the sum of the angles in this Pentagon is because this is a five-sided polygon, right? So we want to find out what this angle plus this angle plus this angle plus this angle plus this angle is equal to. Okay So what we do, we say, okay, let's break up this Pentagon into Triangles because we know the sum of angles in a triangle is 180 degrees, right? So I'm gonna kill this so it's not as busy, right? So start up one node and make a triangle. So you can't make a triangle there That's just a straight line. So there's one triangle and then you already used up this one We want to here and then draw another line to there right? And then that's all we can do. We can make three triangles, right? So one two three triangles. Well, what's the sum of the angles in this Pentagon? Three times 180 because each one of these is 180, right? So three times 180 is basically 180 added to this because we just added one more 180 to a four-sided one, right? There was two here One two. Now there's three, right? If we add these so we get zero Four one goes up. So 540 degrees Right? That's what the angles in a Five in a Pentagon look like. Okay, this is scary now because it looks complicated. He is helping me. I would have drawn five Fun. Now take a look at this thing. You would have drawn five. Yeah, you don't want to draw five Now take a look at this thing. Let's figure out Okay, a possible formula for us to figure out what the sum of the angles in a Higher-sided Polygon is like six-sided or seven-sided or eight-sided, right? So let's do Yeah, one two three four five six question What's the sum of the angles in a six-sided? Polygon right in a six-sided Polygon. Okay now take a look This was a four-sided Polygon and We had two times 180 This was a five-sided Polygon and we had three times 180 right? This was a three-sided Polygon and we had one times 180 Right, so one triangle Two triangles three triangles, right? Well, what's the pattern that you see? One triangle How many sides did it have? It had three sides, right? Okay Quadrilateral has four sides Pentagon has five sides, right? Now take a look at this thing Here is the formula to figure out what the sum of the angles in any Polygon are, right? You go N, so you say let Let and a let statement in mathematics is your friend let N Okay Equal number of Sides in Polygon and a Polygon is a shape like this that encloses Right, and it can't have jagged ends going in Now take a look So let N equal number of sides in a Polygon So this has got three sides. This has got four sides. This has got five sides, right? Now the way we can come up with the formula is this Patre patre patre, I'm sure it's fun as Haldewa David it just looks complicated because you're new to it. Yeah indeed, right? Once you get into it It's easy. It can be easy. It could be very complicated. You could go into topology, which is Just mind trip, right? How's tWitch explaining this better than my teacher? It's not tWitch, it's tWitch Now take a look. The formula is this sometimes it's a guessing game You massage a formula until it fits, right? For this one You write it down as N Minus two times 180 Okay This is equal to the sum of the angles in a polygon equals sum of Angles in N sided Polygon This is the formula. Let me do this in red You want to write this down if you're studying this N minus 2 times 180 equals the sum of the angles in an N Sided polygon So let's try it out for this. This is six sides, right? So according to this formula sum of the angles sum of Angles is equal to six minus two times 180 which is equal to four times 180 which is equal to 720 degrees If that's the case, let's see if we can it means we're gonna have to be able to make four triangles right Four triangles in this thing. Well, let's try it out One triangle Two triangles Three triangles four triangles one two three four see the pattern a triangle has one triangle inside it a Quadrilateral has two triangles inside it a Pentagon five sided polygon has three triangles inside it is six sided polygon has four triangles inside it Okay, what is a 12 sided try out 12 sided polygon? What's the sum of the angles for 12 sided polygon? So I Don't know how to draw 12 sided polygon one two three four five six seven eight nine ten eleven I Try that again How do you start 12 sided polygon? one two three four five six seven eight nine ten eleven twelve there you go I know it looks like a circle because basically is right. So let's assume this is 12 sided twelve Sided well the sum of the angles sum of Angles is equal to 12 minus 2 times 180 which is 10 times 180 which is equal to 1,800 degrees right How many triangles in a 12 sided polygon? 10 Okay with that I was a circle with that Dodge going Right, so that's the formula Easy, right? That's the formula to figure out the sum of the angles in any sided polygon. Did that make sense? Divide divide divide This is that okay All right now if I was you if I was in grade eight or grade nine I take a screenshot of this right now and have that as a note, right? Because it gives you what you need to be able to do a whole bunch of different types of problems now There's one more level to this math 8th grade man 8th grade Yes, I'm kind of getting it. Awesome. Now watch this She's about to get real for when you go to high school indeed now watch this. I'm gonna erase this this this Okay, and this And we'll just do the remaining work here now a regular polygon Okay, I will take screenshot And you can do it when if you you can re-watch the video and just freeze it at that moment, right? This is a timestamp of 28 minutes. No, when did we start 11? Oh wow 58 minutes into the video 8 p.m. Watch this Regular polygon here's a definition for you regular polygon regular Polygon means all sides Same Link Okay, all sides are the same length Okay, no If all the sides are the same length Okay then What's each one of these angles? Right because the way it works is if I draw you a shape, right? Let's say triangle if I say this is 60 degrees and I say this is 60 degrees Then this side has to equal that side, right? And if that's 60 that's 60 some of the angles in a triangle is 180 60 times 60. Yeah for 90 45 45 works to here. We'll do this Here's 45 45 well some of the angles in a triangle is 180 so 45 plus 45 is 90 90 minus 180 is 90. So this one has to be 90 degrees right Okay, but an angle controls the opposite side So this angle if that's the same as that and that link does the same as that So if I say it's a regular polygon Right, it means all the sides are the same Which means all the angles are the same and if all the angles are the same and the total some of the angles For example in a quadrilateral force four-sided polygons 360 then to find each one you just take 360 divided by four Five-sided polygon you want to find out what each one of these angles is you divide it by five You got five sides six-sided you divide it by six. So the way it works is you go Regular polygon equals all sides all sides the same length, right then all angles are Equal, okay, so once all angles are equal It goes without saying that each angle Sunny Leo 98 is in like Flynn throws us the equation, right? All you do you divide the total Then all angles equal therefore and this is mathematicians Taking shortcuts mathematicians are lazy. They shorten everything, right? So this is angles, right? Instead of writing angles. I draw an angle and put an S on it, right then total Then each angle each That's not an each that's equal each Angle is equal to the total divided by number of sides Well, the total is this formula and the number of sides is N, right and as Sunny Lee sunny sunny Leo says son in Leo 98 says it's going to be the formula is N minus 2 times 180 divided by N That's what each angle is going to be in a regular polygon Okay, is that clear does that make sense and This is the way Formulas are derived Right You come up with one formula You come up with one formula and you build on that one formula based on different Metrics you want to calculate, right? Remember the mathematics we know all of the mathematics we know the mathematics that we've used to send people to the moon Right to come up with technology where I in West Coast of Canada Can live stream a math tutoring session to you wherever you might be is based on five rules five Axioms five rules. We try to explain the big bang