hello welcome back the title of this lesson is called measuring angles this is part one so in the last lesson we've learned what a right angle is what an acute angle is and also what an obtuse angle is remember it's all related to if you're smaller or larger than 90 degrees or if you're exactly equal to 90 degrees in this lesson we're going to actually measure the angle measure between two rays we're going to measure it with an instrument called a protractor so let's say that i'm taking a look at this angle on the board what i'm really doing when i try to find the angle measure here is i'm trying to basically figure out how open these rays are if this uh ray here i j we're actually not here if it were really close to this one here then we would say this is a very small angle because it's not very open and the more and more and more open it gets the larger the angle measure if you get to straight up and down it's a 90 degree angle measure and if you go past 90 degrees then you get over here actually straight across is called 180 degrees so basically this is small angles getting bigger bigger bigger bigger bigger bigger as we go like this the more open the rays are the larger the angle now if you want to measure this angle here we have something called a protractor what you do is you put the corner of the angle call it the vertex right there and then we line one of the rays up here and then the other array kind of extends through the measurement device and we read it here now we have a couple of different numbers scale i know you can't really read this i'm going to show you it's going i'm going to blow it up here but basically what you do is you read the position of this array off of the numbers that are here now again i know it's almost impossible for you to see that so what i've done here is i've redrawn it down below we have the same angle here here's h here's i and here's j and we redrawn it down with my protractor on top of it and so you can read the angles a little bit clip more clearly now in order to solve the problem we want to give three things i want to give the name of the angle the measurement of the angle in degrees and also the classification in other words we want to write down if it's an acute angle an obtuse angle or a 90 degree right angle all right first things first let's take a look at this what is the name of this angle so we have h here we have i here and we have j here so i'm going to call this angle h i j now it's important for you to know when you name angles you can name it h i j or you could name it j i h that's totally fine you can name it in any order you want but the i here the center we call it the vertex of the angle has to be in the middle so either h i j or j i h but i has to be in the middle now let's skip over the measurement to the classification if you notice that if you were to go straight up and down from here the number here goes right through 90 degrees so if the angle were up and down then it would be a 90 degree right angle and it would be called a right angle this is larger than that you can see the numbers are larger here in black so is this an acute or an obtuse angle this is an obtuse angle and we know it's obtuse just because we know that it's bigger than 90 degrees that's it now the only thing we have left to do is write down the actual measurement if you look at the numbers here 0 10 20 30 40 50 60 70 80 90 then 100 but this ray is right between 100 and 110 it may be hard for you to see there but this is exactly between 100 and 110 which means it's going to be exactly 105. so the angle measure here is 105 and for derives we put a little circle here the little circle means we're measuring degrees 105 degrees now you might say what are these numbers in blue here that's because basically you have to read whichever scale makes sense you know this angle is bigger than 90 degrees so you know you have to read the number off that's bigger than 90 degrees this other number between here 70 and here's 80 between 70 and 80 would be 75. basically this inner scale the blue scale is telling me how many degrees from this zero over here so basically this angle here is 105 degrees uh from this ray over here but from this one over here if i were measuring from this from a ray over here it would actually be 75 degrees so the blue scale measures from the right the right zero point here this angle measure and then the black scale measures from this but the the simple way to do it is whenever you're looking at the angle you know if it's a cute or a two so you just you read the correct number off the outside as we have done here and i'll show you as we go uh into the next couple of problems all right so let's take a look at the next problem all right so here we have an angle j k l right and i can name it j k l or i can name it l k j but k has to be in the middle right now if i wanted to measure it i would put a protractor on top and i would line it up and i would read the position of this ray so that's what i've done down here so you can read it more easily this is the exact same angle the vertex k goes in the center and then i need to basically read the position of this ray right here now how would i call this angle j k l you put a little angle symbol this symbol means angle j k l or if i wanted to i could call it angle l k j all right now is this acute or obtuse well straight up and down here would be 90 degrees this is larger than that so just like last time this is also obtuse now what is the measurement of this guy we have to look and see what numbers we see well here is 130 degrees in black exactly and my other choice is 50 degrees of course it can't be 50 because that would be an acute angle this is an obtuse angle has to be larger than 90. so we have to write down 130 degrees and the little degree bubble means that you're measuring degrees now what would be this 50 degree angle measure that would be if i wanted to know the angle from here to this zero point would be 50 degrees that's why the blue numbers are there so we ignore that and we write down 130 degrees and of course it's an obtuse angle all right let's move on to the next uh problem here we have an angle here what would we name this angle we could call it pqr or we could call it rqp either way is fine so we put our protractor on top which is what we have here and we're going to call this angle pqr p q r i call it pqr you can call it angle rqp if you like now is this acute or obtuse well if you think about it this is one of the rays a 90 degree ray would be going straight up and down here and this is way smaller than that so this is way smaller than 90 degrees so this is acute so now we have to measure the angle here what choices do we have here's 10 in blue and 20. right in the middle is 15 degrees right what is my other choice here's 160 and 170 so 165 but 165 is way bigger than 90 that's obtuse we know this is not an obtuse angle it's very small angle it has to be 15 degrees right between 10 and 20. so we write down 15 degrees and that's the final answer so angle pqr at 15 degrees is an acute angle all right here's the next problem we have this angle here we put our protractor on top first of all how would we name this angle we could either call it angle x y z or we could call it angle z y x and so for this one i'm going to call it angle symbol x y z but again you could go the other way y has to be in the middle as you see it here now what is the measurement here we measure from this ray up to this one what are the numbers it goes right through 90 on the black and it goes through 90 on the blue why is that because the blue is measuring the angles from here and that's 90 degrees and the black is measuring the angles if i was coming from the other side and that makes sense because 90 degrees is straight up and down so it should be 90 this way and 90 this way and that also tells us that if you have an angle go all the way over flat to the other side 90 plus 90 is 180 and that's why you have 180 in blue and also 180 in blue but this angle goes through 90 so we call it 90 degrees what kind of angle is a 90 degree angle we call that a right angle any angle that goes up and down like that 90 degrees we call it a right angle all right next problem what uh do we call this angle we have we can call it angle abc or we could call it angle c b a but either way b has to be in the middle so we call it angle a b c call it abc now is this an acute angle or an obtuse angle the right angle would be straight up here to 90 degrees this is larger than that it's way larger so this has to be an obtuse angle now what angle measure is it is we go over here and read we have two choices we can choose 20 degrees or 160 degrees it has to be 160 degrees because it has it's an obtuse angle it's bigger than 90 so we have to read 160 that's the angle measures from this side what does the 20 degree mean that means that would be the angle from here down to here that would be a 20 degree angle very small angle from here to here this is 160 degree angle measure so it's obtuse angle and here is our last problem what angle do we have here we could call it d e f or we could call it angle f e d you can call it either one you want i'm going to call it angle d e f and then we're going to ask ourselves is this obtuse or acute well a right angle would be here but this is larger than that so it has to be obtuse and then we ask ourselves what numbers are we going to read is we look here this is 20 30 this is 40 so right between 30 and 40. this is 35 degrees but it can't be 35 degrees because this is an obtuse angle so what's this reading here 150 and 140 right between 140 and 150 is 145. so it has to be 145 degrees so what we're saying is the angle measure between this ray and this ray is 145 but if i were instead measuring from here down it would be actually this other reading which is 35 degrees there so this is 145 degrees so that is how we measure angles we look at one ray and we use the protractor to read the degree markings off to the other ray we just have to be a little careful about which scale do we read and that's why we have to learn what acute and obtuse angles are what a 90 degree angle is so you know how to read the protractor i'd like you to practice all of these yourself and then follow me on to the next lesson we'll get a little more practice with measuring angles