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Measuring draw angles
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How to use a protractor to measure draw angles
Hello! My name is Maria Miller from MathMammoth.com. In this video we're
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going to study about measuring angles. And now, if you watched my other video, you
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hopefully remember how I showed that an angle has two rays and then you open it
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up. The two rays are the two sides of the angle. You can open it up like this and
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then it will be tracing a circle, an arc of a circle like this, okay? And to
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measure angles people have agreed that the full circle would be 360 degrees and
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so if your angle opens up, let me show you, if your angle opens up at the zero
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angle and goes all the way over here then that would be 360 degrees. If it
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just goes half that way to a straight angle then that's 180 degrees and if it
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goes up this much, it is 90 degrees, the right angle, okay? And so we measure the
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angle comparing to the full circle. If it opened up to a full circle, it would be
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360 degrees. Then if it opens up less than that, we just compare how much of
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the circle it has drawn here or traced here, okay? Compared to the full circle.
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That's how angles are measured. We use a protractor to measure angles because it
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has usually half a circle here marked and it has the numbers for the degrees.
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Mine has two sets of numbers and that's usually the case. One set of numbers
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starts here at zero, goes 10, 20, 30, 40, 50, etc. down over here to 180 and the
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other set of numbers starts here at zero and goes all the way here to 180. Okay? So
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So let's say we want to measure this angle. To do that, I need to position the vertex
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of this angle here in my protractor in a certain point. Okay? Now remember that zero is here.
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For my protractor, zero is here. And here is my zero line, so to speak. In your protractor,
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this might be the zero line. You have to check if the zero is actually here. And then it
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that's going up with the numbers. And find your zero line, and in your zero line there's
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usually a little mark, maybe a little circle or something, where you need to
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position the vertex. In mine there is none, but I know that it's the midpoint
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here with the number 15. This midpoint here I need to position to the vertex.
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And then I need to line up my zero line with one of these. Okay, like this. Now
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it's ready for measuring. And then this is how much my angle has opened, see? From
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here to here. And so I read now over here on the arc of the circle, it is very near
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either 70 or 110 degrees. But you need to know which one, right? Well, here was 0. So
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I read the numbers that are 0, 10, 20, 30, 40, etc. I read the lower numbers on mine
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and come to 70. And this is just a tad more than that, 71 degrees, okay. And most
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protractors have marks here, so you can see the individual degrees. This one just
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goes by fives, each five is marked. Let's measure this angle too. So remember I
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need to line up one of these with my zero line, but this doesn't work, okay. Now
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this, okay, this can work, yes. And the vertex has to be put exactly in this
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middle point here. For me it is like the number 15 there. Line up and okay.
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And now you can imagine the angle open from here to here, right? So this is how
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much of the circle it traces. And I again go with these numbers 10, 20, 30
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something. This is my 35 and so it is 37 degrees. Now let's say we have to draw an
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angle. Draw a 36 degree angle. Okay, it will be very close to this size. To start out,
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just draw a line. It's going to be the one side of your angle, okay? There. And now mark
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your vertex there. So if this is my vertex, then it's going to open up maybe somewhere
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there, okay? Like this much. Something like this and this. And now I do the same as if
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If I was measuring the angle, I need to line up this with my zero line here, and the vertex
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with the correct point, like that.
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Now we'll mark over here where it's 36 degrees, there's 30, 35 and a little over there, okay,
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36 degrees.
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And then I use that mark and just draw a line, the other side of my angle, there.
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Now here's draw a 155 degree angle.
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Now, if you think of this, it's gonna start here, go up to 90 and past 90 over there,
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somewhere here.
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It's an obtuse angle.
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We call angles that are more than 90 degrees, less than 180, over here somewhere, obtuse
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angles, which means like a dull type of angle, whereas these that are less than 90 are called
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acute angles.
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Acute angles, think of it as a sharp angle, sharp point that could come to you and, you
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or cut you or whatever, whereas the dull type of angle, like here, obtuse angle, won't hurt
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so much if you were hit with an object with a dull angle.
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So to draw it, I have to first start out by drawing a line again, okay?
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And now I know that my angle is going to open up from here, up to 90, and some more.
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It's going to be somewhere here, right?
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So again, position the zero line of your protractor with the line you drew, and then the midpoint
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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.
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There.
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So this angle here is the 155 angle, or it would have traced an arc of a circle from here.
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We often mark the arc of a circle here, just a little arc of a circle, okay?
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This is traced arc of a circle up to here, but people often mark it nearer the vertex, like that.
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Lastly I have a triangle, and let's try to measure its angles.
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First angle here, it's easy, it's an acute angle, maybe about 40 degrees.
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I put my protractor like this, and read from here, this was 0, 10, 20, 30, 40.
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See, it's almost 50. Okay, 48 degrees, I would say.
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Next angle. Now, this is where students have difficulty, is placing the protractor just right.
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You know, where do you put it now? You know, okay, this has to be lined up with one of the sides.
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But do you line up it like this? Or where, you know?
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You need to remember, this midpoint has to be put to the vertex, but not like this.
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because then you can't see where the other side hits or touches where you're measuring the angle.
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It needs to be turned like this, for example.
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And there's two ways I can do it. I can put it like this.
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Okay? Vertex at the middle and then the real line here.
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Or I can line up my zero line with this side of the angle like this.
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Two ways to do it for each angle.
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So if I do it like this, here's my zero line, and think of opening the angle.
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It opens a little bit past 90 degrees, so this is an obtuse angle, okay?
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It's that here, over there.
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So 0, 10, 20, go past 90, 100, 110.
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You see, it's between 100 and 110.
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And so, 106.
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And here again, okay, it might be difficult.
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You see, oh, this won't work.
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Can you see why?
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How about this way?
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Now, yes, it will work, okay? This is an acute angle. It's not very much. This is
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my zero line and it opens up only this far. So from zero, I'm sorry, from zero I
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go now with these top numbers 10, 20, 30. Almost 30 degrees, maybe 28. Okay, and now
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you probably know that the angles in a triangle have to add up to 180 degrees.
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Maybe you don't know it, but those of you who know it might notice that my numbers
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don't add up to 180, okay? Because 8 plus 8 is 16, plus 6 is 22. But that is
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because it is so difficult to measure so accurately, to get just, you know, maybe in
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reality this is 47 and a half degrees and I rounded it up. Maybe this is only
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27 degrees or whatever. It's hard to measure accurately, so don't be alarmed
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if some of your angle doesn't get exactly 180 degrees.
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- Idioma/s:
- Etiquetas:
- EducaMadrid
- Autor/es:
- MathMammoth
- Subido por:
- Samuel E.
- Licencia:
- Reconocimiento - No comercial - Compartir igual
- Visualizaciones:
- 89
- Fecha:
- 22 de septiembre de 2013 - 11:58
- Visibilidad:
- Público
- Centro:
- IES JOAQUIN ARAUJO
- Duración:
- 09′ 51″
- Relación de aspecto:
- 1.78:1
- Resolución:
- 640x360 píxeles
- Tamaño:
- 32.03 MBytes
