Sal measures several angles with a protractor. Created by Sal Khan.
This is the video for the measuring angles module because, clearly, at the time that I'm doing this video, there is no video for the measuring angles module. And this is a pretty neat module. This was made by Omar Rizwan, one of our amazing high school interns that we had this past summer. This is the summer of 2011. And what it really is, is it makes you measure angles. And he made this really cool protractor tool here so that you actually use this protractor to measure the angles there. And so the trick here is you would actually measure it the way you would measure any angle using an actual physical protractor. You'd want to put the center of the protractor right at the vertex of where the two lines intersect. You can view it as the vertex of the angle. And then you'd want to rotate it so that, preferably, this edge, this edge at 0 degrees, is at one of these sides. So let's do it so that this edge right over here is right along this line. So let me rotate it. So then-- I've got to rotate it a little bit further, maybe one more. No, that's too far. So that looks about right. And then if you look at it this way, you can see that the angle-- and I don't have my Pen tool here. I'm just using my regular web browser-- if you look at the angle here, you see that the other line goes to 130 degrees. So this angle that we need to measure here is 130 degrees, assuming you can read sideways. So that is 130 degrees. Let me check my answer. Very good, I got it right. It would have been embarrassing if I didn't. Let's do the next question. I'll do a couple of examples like this. So once again, let us put the center of the protractor right at the vertex right over there. And let's get this 0 degrees side to be on one of these sides so that this angle will be within the protractor. So let me rotate it this way. And this really is pretty cool what Omar did with this module. So let's see. Let's do it one more time. That's too far. And so that looks about right. And then you can see that the angle right over here, if we look at where the other line points to, it is 40 degrees. Check answer-- very good. Let's do another one. This is fun. So let's get our protractor right over there. And you don't always have to do it in that same order. You could rotate it first so that the 0 degrees is-- and what you want to do is you want to rotate the 0 degrees to one of the sides so that the angle is still within the protractor. So let's rotate it around. So if you did it like that-- so you don't always have to do it in that same order. Although I think it's easier to rotate it when you have the center of the protractor at the vertex of the angle. So we have to rotate it a little bit more. So 0 degrees is this line. And then as we go further and further up, I guess, since this is on its side, it looks like this other line gets us to 150 degrees. And hopefully you're noticing that the higher the degrees, the more open this angle is. And so this one right over here is 150 degrees. And so let's do that-- 150. Let's do one more. Now let me show you what not to do. So what not to do is-- so you could put the center right over there. And you might say, OK, let me make the 0 go right over on this side, right over here. So if you did that, notice your angle would not be within the protractor. So you won't be able to measure it. And what you're attempting to do is measure this outer angle over here, which is an angle, but that's not the angle that this question is asking us to measure. This little arc over here is telling us that that's the angle that we need to measure. So that arc has to be within the protractor. So let's rotate this protractor a little bit more. I overdid it. And so this looks like this is 0 degrees, and then this right over here is 60 degrees. 60 degrees-- we got that one right, too. So hopefully that helps you with this module. It's kind of fun.