Brian McCall

**Univ. of Wisconsin**

J.D. Univ. of Wisconsin Law school

Brian was a geometry teacher through the Teach for America program and started the geometry program at his school

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In Geometry, it is important to know how to measure an angle. **Using a protractor** helps us determine the angle measurement so we can label it as acute, right or obtuse. Every protractor is a little bit different, but all will have a location on the bottom edge where we align the vertex of the angle we are measuring. After lining up the vertex, we line up the bottom edge of the protractor with one side of the angle and use the marks on the top to measure.

In Geometry it's important to know how to measure an angle. To do that you use a protractor, the key thing about thing about using a protractor is using this alignment. Now every protractor is a little bit different but they're all going to have something at the middle of the base. And that's where you want to put your vertex of your angle. And vertex is spelled with an e and not an a. So that is where the vertex is going to go and then along one of these two bases, so either the distance between this center and the edge over here or this center and the edge over here, that is where one of the sides of your angle is going to go. So you're going to have one of your sides and the vertex all lined up.

And then you're going to have some sort of ray that's going to extend all the way so that you can get a measure. Now one key thing that students kind of forget is let's say you're measuring an angle, that only goes there, same as [IB] I'm going to guess but I'm not really quite sure what the angle measure is. What you need to do then, is to grab your straight edge so I'm going to grab mine and you're just going to extend that ray. And extend it all the way until you can actually give yourself a very accurate reading of the degree measure.

Now the last key thing that you need to take in mind is obtuse, acute or a right. Before you even measure an angle kind of eye ball it and make a guess and if you look at this angle right here it's pretty clear that this is going to be obtuse. It's more than 90 degrees so when you're going to use these measures there's always going to be two numbers. One is going to be larger than 90, one is going to be smaller than 90. So when I use my protractor to measure this, because I know this is obtuse, I'm going to take the larger number. So I'm going to grab my protractor and again mine is going to look a little different it is designed for use on white boards. And so what I'm going to do because I'm going to place whatever this little center is along right at the vertex and I'm going to make sure that one of these bases right here is along this bottom side.

And then I'm going to say "well where does this other ray cross the edge of my protractor?" And I see that, that distance, if here is 90 so we're going up so we have 120 right here and I have a 135 right here. So the question is this 137 or is it 132. Well if I look my numbers are increasing as I go further and further away from 90 degrees so I'm going to be 2 back from 135 or it's going to be 133 degrees, okay? And that confirms my original suspicion that this was an obtuse angle.

Let's try measuring another one, so if I measured this angle right here I'm going to guess that it's right but I'm not quite sure. So I'm going to put the center of my protractor on the vertex and I'm going to make sure that one of my bases is aligned and it looks like we have something that's a little bit over 90 degrees, which means that's going to be obtuse and when I measure it I see that we're going to have about 91.5 degrees. Now you really aren't going to be able to be accurate to the 10th place. If you come up with a number saying "oh Mr. McCall I got this angle is 91.508 degrees" I'm going to say "you don't have enough information on your protractor to go that far out on your decimal place." So I'd say if it's in between you can make an estimate on your 10th place but otherwise you can just round this and say that this is about 92 degrees.

So this last one is very clearly acute it's going to be less that 90 degrees so when I look at my protractor I know I'm going to be using the smaller number. So again you put the center right down our vertex and then you align one of these bases at one of the sides of your angle, and it's pretty clear that we have a little less than 60 degrees according to what I can see and we're going to say that this angle right here is going to be 58 degrees. So the key to using your protractor, remember there's about 3, first is align whatever center hole that you have of your protractor, on the vertex. Second key thing is align one these edges along the side of your angle and the last key thing is make a guess about the size of the angle and that'll tell you which number to use. If you're shown this problem on a quiz and you said "no Mr. McCall that is 57 degrees" I'm going to say "that's wrong because although the marking might have been correct you didn't recognize this as obtuse and it should've been 133 degrees."