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# Intro to angles (old)

## Video transcript

hello in this series of presentations I'm going to try to teach you everything you need to know about triangles and and angles and parallel lines and this is probably the highest yield information that you could ever learn especially in terms of a standardized test and then when we've learned all the rules we'll play something that I called the angle game which is essentially what the SAT makes you do over and over again so let's start with some basics well you know what an angle is well actually maybe you don't know what an angle is and I'll tell you what an angle is an angle if I have two lines let me draw a thicker line than that if I have two lines and they intersect at some point the angle is a measure of exactly kind of how how wide the intersection is between those two lines so it's like let me use a better tool so this is the angle an angle is is how wide those two lines kind of open up and they're measured either in degrees or radians and and for the sake of most of a geometry class will use it degrees and that's in when we start doing trigonometry you learn radians or maybe you could learn it now and you're probably familiar with this you know a very small zero degrees would be these two lines on top of each other this if I were to just eyeball it looks like I don't know like 45 degrees if I had the lines even wider apart like that that's 90 degrees and a 90 degree lines are also called perpendicular because they are well I feel like saying because they are perpendicular but because one is going completely vertical while the other is going horizontal they're going in in they well it's actually amazingly difficult to find the exact right wording but I think you get the idea there by definition perpendicular lines have a 90 degree apart from each other and you know you've seen this all the time and things like squares and you know rectangles if I were to draw a rectangle like that all right a rectangle is made up of a bunch of perpendicular lines or lines at 90-degree angles so example these two lines are at a 90 degree angle the way you draw a 90 degree angle is you draw a little box like that that's the same thing as doing this is doing a 90 degree angle and you can even get wider angles so if you go above 90 degrees so let me draw so let's say I had a lines like this so this would be I don't know I'm just eyeballing it 135 degrees or something like that and you could if you if you ever want to really measure the angles you can use something called a protractor that's a tool maybe your teachers can help you use that for that would be 135 degrees and then if you had a complete if you had it so wide that the two lines are actually almost forming a line then this becomes 180 degrees it's almost like one line right this is 180 degrees and then you can keep going you could go with the so this if this angle here is 135 degrees you can actually also measure this angle right here let me do it in a different color just to add some variety so then this angle right here so the angles in a circle aren't they're 360 degrees in a circle so if this is 135 this blue and this I don't know my colors this magenta angle would be 360 degrees minus 135 degrees and that's equal to what that's 225 degrees is this is this magenta angle and then we can do other things like that so one you know that the degrees in the circle are 360 degrees this is important to note degrees in the circle are 360 degrees it's also important to know that if you just go kind of halfway around a circle like we did here that's 180 degrees like if you viewed the pivot point is like let's say right here I mean looks like just one line and it really is but that's 180 degrees and then if you go quarter way around the circle that's 90 degrees all right hopefully you're getting a bit of an intuition for for what an angle is so now I will teach you a bunch of very useful rules for angles clear this so let me redraw so if I had a line like this I like using the colors just so I think it'd keep you from getting completely bored and that it might not be completely intuitive what I'm doing but let's add an angle like that and so let's just say you know I'm not measuring these exactly let's say that this is 30 degrees we know that if we go all the way around the circle if we go all the way around the circle we know that that's 360 degrees all right and that's a very ugly looking around the circle angle that I drew so then we also know that this this angle right here is 330 degrees right because this angle Plus this magenta angle is going to equal the whole circle so this is equal to 330 degrees so the angles in the circle so remember that the angles in a circle or there are 360 degrees in the circle and if if you ever played I don't know if you if you were member you probably don't the subscribe before you were born where there used to be a game called 720 and it was a skateboarding game it was a video game and the 720 was essentially you were you know you try to jump your skateboard and and spin around twice and that's why it's a 720 degrees if you spin around if you go around in the circle twice at 720 degrees if you just jump and spin around once you went 360 degrees so that's where you probably heard this in just you know popular culture but anyway so 360 degrees in a circle and you could imagine half a circle is 180 degrees and so the other important thing to realize is like we said if we go halfway around the circle it's 180 degrees but if we have two angles that add up to that so let's say I don't know if these lines were thick enough for you to see let me draw something well doesn't look ideal but you get the idea so if you have this line this angle of whoops I'm still using my line tool if we have this angle is I don't know let's call it X and then this and then this angle is y what do we know about the relationship between x and y well we know that this we know that the entire angle is half of a circle right so that's 180 degrees that's 180 degrees this entire angle so what are angles X and y going to add up to well X plus trying to stay color consistent X plus y are going to equal I don't know if I'm color blind I think are going to equal 180 degrees or you could write you know Y is equal to 180 minus X or X is equal to 180 minus y but if X plus y is equal our are equal to 180 degrees and you can see that it makes sense that they do they kind of if you add the two angles you go halfway around the circle then that tells us that x and y are and this is a fancy word and it's just good to commit this to memory they are supplementary supplementary angles supplementary supplementary supplementary angles that's when you add to 180 degrees now what if we had this situation oh my god that was horrible do a new let's I had this situation let's see I draw two perpendicular lines right so this is going a quarter way around the circle all right let's say this entire angle here this entire angle I'm trying it really big that's 90 degrees right there perpendicular and now if I had two angles within that so now if I have two angles here so let's say that this is X and this is y what do x and y add up to well X plus y is 90 and we can say that x and y are complementary complementary it's important to not get confused between the two just remember complementary means two angles add up to 90 degrees supplementary means that two angles add up to 180 degrees I'm running out of time so I will see you in the next video