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### Course: Basic geometry and measurement > Unit 3

Lesson 5: Measuring angles# Measuring angles using a protractor

Learn to use a virtual protractor to measure angles. Created by Sal Khan.

## Want to join the conversation?

- Who invented the protractor(39 votes)
- Thomas Blundeville invented the protractor.(22 votes)

- Good question. 360º and 0º will be on the same place on a diagram, but they mean different things. Think of it this way. You walk onto a basketball court and step onto one of the painted circles. You have just stepped on the circle, so you have traveled 0º around the circle. Now you walk along the circle. When you have walked halfway around it you have traveled 180º. When you have walked all the way around the circle you have traveled 360º. You are in exactly the same physical place that you were when you started at 0º, but saying that you are at 360º tells people that you have traveled around the circle.(34 votes)

- does the angle have to be 100% accurate?(12 votes)
- For example, imagine that you are taking a point in the map. A simple 1 degree error, in 1 mile, that represents easily more than 10m in topographic (depending of the scale of the map). If you go to the astronomy area in NASA, 1 degree is an unacceptable mistake for the engineers.(9 votes)

- Is a angle used in everyday life?(10 votes)
- By humans? Of course. Maybe by nature as well... A leading theory on why moths follow light is based on the concept that the moth keeps a constant angle to the Moon (theta) to navigate at night. Introduce a closer light and the angle is compromised; hence the Moth circling in towards a light bulb. Since the moon is so far away the angle to the moth is relatively the same.(13 votes)

- are there negative angles, and if so is there a protractor that will measure them?(13 votes)
- no, there are no negative angles. once they go all the way around and pass the point, it goes back to 0 and starts all over again.(5 votes)

- Do you really need a protractor to see the degree? Is it really hard to tell by a human eye?(7 votes)
- You can guess with the human eye, but using a protractor will give you a more precise answer.(10 votes)

- What grade is this for?(7 votes)
- Hey, Josiah! This is material for fourth grade, at least in Common Core.(8 votes)

- what would the angle be called if it were smaller than 90 degrees?(7 votes)
- Good question, since we know that anything that is beyond a 90 degree angle is called an Obtuse angle, then what would the angle be called if it were smaller than 90? To answer your question, it would be called an Acute angle, it would mean 1, 2, 3, 4, etc. degree angles. I hope this helped!(2 votes)

- At1:18,why do all of the angles have to be at 0 degrees?(7 votes)
- They don't. You can start at any angle but it would be harder because you would have to subtract the small number from the larger one; so that's why most people start at the 0 degree mark: you don't have to any extra math.(8 votes)

- Why is the largest angle 360 degrees? Why can't the largest angle be...... say 500 degrees?(7 votes)
- That would go into negatives(3 votes)

## Video transcript

What I have right in front
of me is the Khan Academy measuring angles exercise. I have a small part of it in
this screen right over here. And it's a pretty cool
exercise because it has this little
virtual protractor that we can use to
actually measure angles. And I want to give
credit to the person who built this protractor, because
I think it's pretty neat. Omar Rizwan, who was actually
a high school intern, made this pretty neat module. And so in general, when you
want to measure an angle, what you want to do
is you want to put the center of your
protractor at the center of-- or I should say, at the
vertex of the angle. Or you want to put the
vertex of the angle at the center of the protractor. And then what you want to do
is either rotate the angle or rotate the protractor. In this case, we're going
to rotate the protractor. You want to rotate
the protractor so that the 0 angle,
or kind of the 0 mark, is at one of the
sides of the angle. And the other side of the
angle is within the protractor. So let's try to do that. So maybe if we want to
do that, this 0 side should be at this
side of the angle. So let's rotate it that way. Let me just keep rotating it. If I could just keep it pressed. That's better. All right. That looks about right. So one side is at the 0 mark. And then my angle,
my other side-- or if this was a
ray, it points to, looks like, pretty close
to the 20 degree mark. So I will type that
in off the screen. You don't see that. And that is the right answer. And then we can
get another angle. So let's try to measure
this one right over here. So once again, place the
center of the protractor at the center, at the
vertex, of our angle. We can place the 0 degree,
the base of the protractor, at this side of the angle. So let's just rotate it a
little bit, maybe one more time. That looks about right. And then the angle is now
opening up-- let's see, the other side is
pointing to 110 degrees. So this is larger
than 90 degrees. It's also an obtuse angle. The last one was an acute angle. This is obtuse, 110 degrees. More than 90 degrees. So let me type it in. I got the right answer. Let's do a couple more of these. So once again, put the
center of the protractor at the vertex of our angle. And now, I want to rotate it. There we go. And this looks like roughly
an 80 degree angle, not quite. If I have to be
really precise, it looks like it's maybe
81 or 82 degrees. But I'll just go with
80 as my best guess. I got the right answer. Let's do one more of these. So once again,
vertex of my angle at the center of my protractor. And then I want to put one side
of the angle at the 0 degree. And I want to show you,
there's two ways to do that. You could do this. You could do just this. But this isn't too helpful,
because the angle is now outside. The other side sits
outside of the protractor. So you want the 0
degrees on the side, so the other side is
within the protractor. So let's keep rotating it. There we go. And then our other
side opens up or you could say points to 70 degrees. So this is an acute
angle right over here. So it is 70 degrees. So I'll leave you with that. Oh look, I'm ready to move
on, the exercise tells me. And now we can start talking
about more things about angles now that we know
how to measure them.