1 00:00:00,180 --> 00:00:04,740 Hello! My name is Maria Miller from MathMammoth.com. In this video we're 2 00:00:04,740 --> 00:00:10,080 going to study about measuring angles. And now, if you watched my other video, you 3 00:00:10,080 --> 00:00:15,300 hopefully remember how I showed that an angle has two rays and then you open it 4 00:00:15,300 --> 00:00:20,219 up. The two rays are the two sides of the angle. You can open it up like this and 5 00:00:20,219 --> 00:00:26,960 then it will be tracing a circle, an arc of a circle like this, okay? And to 6 00:00:26,960 --> 00:00:32,740 measure angles people have agreed that the full circle would be 360 degrees and 7 00:00:32,740 --> 00:00:38,920 so if your angle opens up, let me show you, if your angle opens up at the zero 8 00:00:38,920 --> 00:00:47,630 angle and goes all the way over here then that would be 360 degrees. If it 9 00:00:47,630 --> 00:00:54,390 just goes half that way to a straight angle then that's 180 degrees and if it 10 00:00:54,390 --> 00:01:01,409 goes up this much, it is 90 degrees, the right angle, okay? And so we measure the 11 00:01:01,409 --> 00:01:07,150 angle comparing to the full circle. If it opened up to a full circle, it would be 12 00:01:07,150 --> 00:01:12,250 360 degrees. Then if it opens up less than that, we just compare how much of 13 00:01:12,250 --> 00:01:18,609 the circle it has drawn here or traced here, okay? Compared to the full circle. 14 00:01:18,609 --> 00:01:23,670 That's how angles are measured. We use a protractor to measure angles because it 15 00:01:23,670 --> 00:01:31,909 has usually half a circle here marked and it has the numbers for the degrees. 16 00:01:31,909 --> 00:01:36,629 Mine has two sets of numbers and that's usually the case. One set of numbers 17 00:01:36,629 --> 00:01:42,870 starts here at zero, goes 10, 20, 30, 40, 50, etc. down over here to 180 and the 18 00:01:42,870 --> 00:01:50,170 other set of numbers starts here at zero and goes all the way here to 180. Okay? So 19 00:01:50,170 --> 00:01:56,209 So let's say we want to measure this angle. To do that, I need to position the vertex 20 00:01:56,209 --> 00:02:03,849 of this angle here in my protractor in a certain point. Okay? Now remember that zero is here. 21 00:02:03,849 --> 00:02:10,789 For my protractor, zero is here. And here is my zero line, so to speak. In your protractor, 22 00:02:10,789 --> 00:02:14,949 this might be the zero line. You have to check if the zero is actually here. And then it 23 00:02:14,949 --> 00:02:21,129 that's going up with the numbers. And find your zero line, and in your zero line there's 24 00:02:21,129 --> 00:02:24,250 usually a little mark, maybe a little circle or something, where you need to 25 00:02:24,250 --> 00:02:28,689 position the vertex. In mine there is none, but I know that it's the midpoint 26 00:02:28,689 --> 00:02:33,250 here with the number 15. This midpoint here I need to position to the vertex. 27 00:02:33,250 --> 00:02:46,580 And then I need to line up my zero line with one of these. Okay, like this. Now 28 00:02:46,580 --> 00:02:52,460 it's ready for measuring. And then this is how much my angle has opened, see? From 29 00:02:52,460 --> 00:03:00,960 here to here. And so I read now over here on the arc of the circle, it is very near 30 00:03:00,960 --> 00:03:07,639 either 70 or 110 degrees. But you need to know which one, right? Well, here was 0. So 31 00:03:07,639 --> 00:03:12,259 I read the numbers that are 0, 10, 20, 30, 40, etc. I read the lower numbers on mine 32 00:03:12,259 --> 00:03:20,659 and come to 70. And this is just a tad more than that, 71 degrees, okay. And most 33 00:03:20,659 --> 00:03:26,319 protractors have marks here, so you can see the individual degrees. This one just 34 00:03:26,319 --> 00:03:32,719 goes by fives, each five is marked. Let's measure this angle too. So remember I 35 00:03:32,719 --> 00:03:41,539 need to line up one of these with my zero line, but this doesn't work, okay. Now 36 00:03:41,539 --> 00:03:47,360 this, okay, this can work, yes. And the vertex has to be put exactly in this 37 00:03:47,360 --> 00:03:54,139 middle point here. For me it is like the number 15 there. Line up and okay. 38 00:03:54,139 --> 00:03:58,819 And now you can imagine the angle open from here to here, right? So this is how 39 00:03:58,819 --> 00:04:02,659 much of the circle it traces. And I again go with these numbers 10, 20, 30 40 00:04:02,659 --> 00:04:11,129 something. This is my 35 and so it is 37 degrees. Now let's say we have to draw an 41 00:04:11,129 --> 00:04:18,129 angle. Draw a 36 degree angle. Okay, it will be very close to this size. To start out, 42 00:04:18,670 --> 00:04:25,670 just draw a line. It's going to be the one side of your angle, okay? There. And now mark 43 00:04:26,509 --> 00:04:31,689 your vertex there. So if this is my vertex, then it's going to open up maybe somewhere 44 00:04:31,689 --> 00:04:37,329 there, okay? Like this much. Something like this and this. And now I do the same as if 45 00:04:37,329 --> 00:04:42,709 If I was measuring the angle, I need to line up this with my zero line here, and the vertex 46 00:04:42,709 --> 00:04:46,829 with the correct point, like that. 47 00:04:46,829 --> 00:04:53,329 Now we'll mark over here where it's 36 degrees, there's 30, 35 and a little over there, okay, 48 00:04:53,329 --> 00:04:54,329 36 degrees. 49 00:04:54,329 --> 00:05:02,990 And then I use that mark and just draw a line, the other side of my angle, there. 50 00:05:02,990 --> 00:05:07,269 Now here's draw a 155 degree angle. 51 00:05:07,269 --> 00:05:13,509 Now, if you think of this, it's gonna start here, go up to 90 and past 90 over there, 52 00:05:13,509 --> 00:05:14,509 somewhere here. 53 00:05:14,509 --> 00:05:15,509 It's an obtuse angle. 54 00:05:15,509 --> 00:05:21,589 We call angles that are more than 90 degrees, less than 180, over here somewhere, obtuse 55 00:05:21,589 --> 00:05:27,129 angles, which means like a dull type of angle, whereas these that are less than 90 are called 56 00:05:27,129 --> 00:05:28,810 acute angles. 57 00:05:28,810 --> 00:05:36,480 Acute angles, think of it as a sharp angle, sharp point that could come to you and, you 58 00:05:36,480 --> 00:05:42,300 or cut you or whatever, whereas the dull type of angle, like here, obtuse angle, won't hurt 59 00:05:42,300 --> 00:05:46,740 so much if you were hit with an object with a dull angle. 60 00:05:46,740 --> 00:05:53,100 So to draw it, I have to first start out by drawing a line again, okay? 61 00:05:53,100 --> 00:05:57,420 And now I know that my angle is going to open up from here, up to 90, and some more. 62 00:05:57,420 --> 00:06:00,680 It's going to be somewhere here, right? 63 00:06:00,680 --> 00:06:07,259 So again, position the zero line of your protractor with the line you drew, and then the midpoint 64 00:06:07,259 --> 00:06:18,459 And now I have to go past 90 to 100, 110, all the way to 150, 155, over here, and draw a mark, and then draw my line. 65 00:06:20,899 --> 00:06:21,120 There. 66 00:06:21,939 --> 00:06:29,459 So this angle here is the 155 angle, or it would have traced an arc of a circle from here. 67 00:06:30,199 --> 00:06:34,959 We often mark the arc of a circle here, just a little arc of a circle, okay? 68 00:06:34,959 --> 00:06:40,959 This is traced arc of a circle up to here, but people often mark it nearer the vertex, like that. 69 00:06:40,959 --> 00:06:44,959 Lastly I have a triangle, and let's try to measure its angles. 70 00:06:44,959 --> 00:06:52,959 First angle here, it's easy, it's an acute angle, maybe about 40 degrees. 71 00:06:52,959 --> 00:07:02,959 I put my protractor like this, and read from here, this was 0, 10, 20, 30, 40. 72 00:07:02,959 --> 00:07:06,560 See, it's almost 50. Okay, 48 degrees, I would say. 73 00:07:08,680 --> 00:07:13,779 Next angle. Now, this is where students have difficulty, is placing the protractor just right. 74 00:07:14,279 --> 00:07:19,920 You know, where do you put it now? You know, okay, this has to be lined up with one of the sides. 75 00:07:20,079 --> 00:07:23,540 But do you line up it like this? Or where, you know? 76 00:07:24,600 --> 00:07:28,959 You need to remember, this midpoint has to be put to the vertex, but not like this. 77 00:07:28,959 --> 00:07:36,959 because then you can't see where the other side hits or touches where you're measuring the angle. 78 00:07:36,959 --> 00:07:40,959 It needs to be turned like this, for example. 79 00:07:40,959 --> 00:07:44,959 And there's two ways I can do it. I can put it like this. 80 00:07:44,959 --> 00:07:48,959 Okay? Vertex at the middle and then the real line here. 81 00:07:48,959 --> 00:07:53,959 Or I can line up my zero line with this side of the angle like this. 82 00:07:53,959 --> 00:07:56,959 Two ways to do it for each angle. 83 00:07:56,959 --> 00:08:01,939 So if I do it like this, here's my zero line, and think of opening the angle. 84 00:08:02,300 --> 00:08:05,959 It opens a little bit past 90 degrees, so this is an obtuse angle, okay? 85 00:08:06,720 --> 00:08:08,060 It's that here, over there. 86 00:08:08,420 --> 00:08:11,160 So 0, 10, 20, go past 90, 100, 110. 87 00:08:12,000 --> 00:08:13,660 You see, it's between 100 and 110. 88 00:08:14,879 --> 00:08:16,540 And so, 106. 89 00:08:20,660 --> 00:08:23,000 And here again, okay, it might be difficult. 90 00:08:23,480 --> 00:08:25,220 You see, oh, this won't work. 91 00:08:26,980 --> 00:08:27,660 Can you see why? 92 00:08:32,889 --> 00:08:33,570 How about this way? 93 00:08:33,570 --> 00:08:43,830 Now, yes, it will work, okay? This is an acute angle. It's not very much. This is 94 00:08:43,830 --> 00:08:53,940 my zero line and it opens up only this far. So from zero, I'm sorry, from zero I 95 00:08:53,940 --> 00:09:05,269 go now with these top numbers 10, 20, 30. Almost 30 degrees, maybe 28. Okay, and now 96 00:09:05,269 --> 00:09:10,129 you probably know that the angles in a triangle have to add up to 180 degrees. 97 00:09:10,129 --> 00:09:14,350 Maybe you don't know it, but those of you who know it might notice that my numbers 98 00:09:14,350 --> 00:09:20,850 don't add up to 180, okay? Because 8 plus 8 is 16, plus 6 is 22. But that is 99 00:09:20,850 --> 00:09:27,490 because it is so difficult to measure so accurately, to get just, you know, maybe in 100 00:09:27,490 --> 00:09:31,450 reality this is 47 and a half degrees and I rounded it up. Maybe this is only 101 00:09:31,450 --> 00:09:35,889 27 degrees or whatever. It's hard to measure accurately, so don't be alarmed 102 00:09:35,889 --> 00:09:40,549 if some of your angle doesn't get exactly 180 degrees.