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Hi, today we're going to be measuring angles using a protractor.

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Sometimes we use a full-size protractor and sometimes we use a half protractor.

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The half protractor is much more common, so our goal is to learn to use that.

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So first we have to talk about what an angle is.

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An angle is formed by two rays, or line segments, and do you remember

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what the end point is called? That's right, it's called a vertex.

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That's where the lines, or line segments, or rays meet.

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There are three types of angles, three you've learned in the past.

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A cute angle is smaller than 90 degrees, a right angle is exactly 90 degrees,

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and an obtuse angle is greater than 90 degrees, but less than 180 degrees.

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In fourth grade, we learn about a new type of angle called a reflex angle.

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A reflex angle is greater than 180 degrees.

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The first thing you need to do when measuring angles is estimate the measure of the angle.

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This one should be pretty easy. This one is a 90 degree angle. What about this one?

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You can use what you know about angles on clocks to help you figure out that

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this one is a 30 degree angle. This one is a little harder. We know that it's

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greater than 90 degrees but less than 180 degrees. We could estimate this one.

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What would you guess? If you guessed close to 150 degrees you did a great job.

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What about this one? 120 degrees. You had to know that the measure the angle I was

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measuring was this inside angle and not the outside angle. We'll look at that

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later when we look at showing a directional arrow. So you can use a full

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protractor to help you measure angles. A full protractor starts at zero and

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measures all the way around. Here's 180 degrees, 270 and all the way back up to

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360. There are 360 degrees in a circle and a protractor is just a circle. You

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can also use a regular protractor to measure angles. When you take a look at

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this one, notice that there are two sets of numbers. One number on the inside has

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a zero starting on the right. You can measure up to 90 degrees and then angles

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greater than 90 degrees on this side all the way to 180. On the outside, you have a zero

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on the left, and use the outside numbers to measure this way, all the way up to 90, and

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then continue on all the way up to 180. What you need to know when measuring angles is

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where the baseline is. The baseline will always line up to zero degrees on the protractor.

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You also need to know where the vertex of the angle is, because that must line up with

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center of the protractor. So where is the baseline? Our angles will have directional

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arrows as you can see on these two angles. The baseline is where the directional arrows

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begin. So on this one, the baseline is this line where the directional arrow begins. And

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on this one, can you tell where the baseline is? Yep, it's this line segment where the

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directional arrow begins. So we will measure this angle on the right from here around this

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way. So how do you use your protractor to measure the angle? Well the first thing

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you need to do is place the dot on your protractor over the vertex of the angle

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and line zero degrees to the baseline. The second line array tells how many

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degrees the angle is open and that's how we measure the angle. So let's try

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measuring. The first thing we'll do here is open up our protractor. This is a full

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circle protractor. The first thing I want to do is put the middle of the

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protractor right on the vertex of my angle and then I want to line up my

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baseline to zero. Now that I have my baseline lined up to zero I can look at

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my other line and see that it's not quite long enough to go to the other

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side of the protractor. What we do then is we can I could make the protractor

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smaller but on paper you could just extend the line and now I can clearly see that this is a 25

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degree angle that makes sense to me because I know that a 90 degree angle is a right angle and this

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one is much smaller less than half the size of a 90 degree angle so the measure of this angle is

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25 degrees well what about this one I'm going to line up the vertex of the angle with the center

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of my protractor and then I'm going to turn my protractor so zero degrees lines up with

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the baseline and I'm going to use the line on the right to show my baseline to zero degrees.

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Now the angle I'm measuring is this angle. I know that that angle is greater than ninety

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degrees so when I look at my other line, actually it's a ray, I see that there are two numbers

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it could be. Is that angle between 230 degrees and

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240 degrees like the top numbers say? Or between 120

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and 130 degrees? Well my reasoning tells me that it's probably

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between 120 and 130 degrees because it's

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greater than a 90 degree angle, but less than a 180 degree

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angle. So when I count up here, I see that that is a

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126 degree angle.

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So I can write on my line 126 degrees.

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I have to put a little dot there to show degrees.

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Now we can also use a half-circle protractor to do the same thing.

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So I'm going to switch over here to a half-protractor.

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Now you can see that there are two sets of numbers.

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You have to use your reasoning before you start using the protractor.

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You have to look at the angle and know that it's less than a 90-degree angle.

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So the measurement has to be less than 90 degrees.

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So I'm going to move my protractor down so that the vertex is right at that cross.

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And then I need to line up the baseline with 0 degrees.

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Now when I look at this other line segment, I can see that it's between 20 and 30 degrees.

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I know it's not 150 to 160. That just wouldn't make sense.

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And so when I count the little degrees in between 20 and 30,

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I can see that that angle is a 26 degree angle.

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When I use my half protractor on this one, I need to use my reasoning again.

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I know that this angle is greater than 90 degrees.

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So when I put my protractor on this baseline at 0, I see 0 is on the inside.

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So I'm going to use the inside numbers as I count up.

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And I see it's between 120 and 130 degrees.

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degrees, but it's closest to 126 degrees. That makes sense. So why don't you go ahead

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and try measuring some angles on your own.