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## 4th grade

### Course: 4th grade > Unit 11

Lesson 2: Angle introduction# Acute, right, & obtuse angles

CCSS.Math:

Acute angles measure less than 90 degrees. Right angles measure 90 degrees. Obtuse angles measure more than 90 degrees. Learn about angles types and see examples of each. Created by Sal Khan.

## Want to join the conversation?

- How do I label a line straight a cross?(25 votes)
- A straight line is 180 degrees, or a "straight" angle. Since it continues forever in both directions, it can also be considered a line.(22 votes)

- is there a angle more than 360 degrees(11 votes)
- No, if you pass 360 degrees, the angles rolls over and starts at 0 again. So, if you had a supposed 365 degree angle, it would really just be a 5 degree angle(31 votes)

- Is 190 degrees still considered an obtuse angle?(9 votes)
- No it is not because obtuse angles are more than 90 degrees but less than 180. Degrees above 180 and under 360 are reflex angles. 190 degrees are more than 180 so we cannot call it an obtuse angle but we can call it as reflex.(4 votes)

- Can angles be larger than 360 degrees or do they keep going back to 0 degrees in a circle?(5 votes)
- In basic geometry, an angle is the "opening" between two rays. But if we talk about angles greater than 360 degrees, this cannot happen BETWEEN two rays.

It is possible to ROTATE one ray around an axis away from another ray so that it goes all the way around and meets the original ray (360 degrees) - then you could rotate it another 90 degrees to come up with a ROTATION of 450 degrees. Hope that makes sense!(17 votes)

- an acute angle measure less than 90 degrees. right angle measures 90 degrees. obtuse angle measures more than 90 degrees(8 votes)
- easy way to remember these acute a cute little angle right square in the middle and obtuse big angle(8 votes)
- What is obtuse?(2 votes)
- an angle that is greater than 90 degrees and shorter than 180 degrees.(11 votes)

- Is there another way to write the less than/greater than? It looks to me like a angle sign and I'm worried I'm going to be confused going over my notes later (For now I'm just writing less than/equal then but I wanted to know if there was a shorter form then < > I doubt it though)(4 votes)
- There isn't another way. One thing that will help you, though: the less than/greater than symbol will not be lying on the 'ground'; the angle sign will be.(5 votes)

- What other angles are there other than Acute, Obtuse, Right?(4 votes)
- A straight angle measures 180º.

A reflex angle is between 180º and 360º.(6 votes)

- If I was to classify right angles as either obtuse or acute angles, which would I classify them as?(3 votes)
- Neither. Acute angles are less than 90 degrees, obtuse angles are more than 90 degrees, and right angles are exactly 90 degrees.(7 votes)

## Video transcript

In this video, I
really just want to introduce you
to some terminology for some basic angle types. And the terminology I
want to introduce you to are acute angles, right
angles, and obtuse angles. And I think when we
just go through these, they'll be pretty
self-explanatory. An acute angle is an
angle-- well, let me just draw them first. Then it might start
to make sense. So an acute angle will
look something like that. I draw two rays that are
coming from a common point. So the acute angle will be
this angle right over here. I could also draw an
acute angle, maybe an angle that's formed from
the intersection of two lines. This angle will be acute,
and so will this angle. They're both acute angles. And we're going to see is
acute angles are ones that are-- since I haven't defined
right angles yet-- they're narrower. And what we're going
to see is that they're smaller than right angles. Right angles are when the
rays or the lines are going, I guess, in the-- I don't
want to use the word, right, in my definition-- but if
one is going horizontal, the other one will
be going vertical. So let me draw it
with the rays first. So the right angle, this
one's going from the left to the right. Then the other ray is going
from the bottom to the top. This angle right over
here is a right angle. And I could label it like
that, as a traditional angle. But the general convention
for labeling right angles is to put a little, kind of a
half of a box right over there. And that means that
is a right angle. Or that if this is
going left to right, this is going perfectly
top to bottom, that this is in no way kind of--
I guess the best way to think about it and why
it's called right is that this ray is
completely upright, compared to this ray over here. And let me draw it
with some lines. So if I have one line
like this and then I have another line like
that, a right angle over here-- actually
all of these would have to be right angles--
it would mean that this line is completely-- if
this was the ground, this line is completely
upright, relative to this line over here. So either of these, that's
what a right angle means. And now that we've
defined right angle, I can give you another
definition for an acute angle. An acute angle has a
measure, or it's smaller, than a right angle. When you learn about
radians and degrees, which are different ways
to measure angles, you'll see that a right angle
can be measured as 90 degrees. This over here is
less than 90 degrees. So this is less than 90 degrees. And one way to
conceptualize this is that this angle, its opening
is smaller, it's more narrow, the lines are-- you would
have to rotate one line less to get to the other line
than you would over here. Here, you'd have to move
it all the way over there. Here, you'd only have
to move it a little bit. So the acute angle is
less than a right angle. And so you might imagine
already what an obtuse angle is. It is greater than
a right angle. So let me draw a couple of
examples of obtuse angles. So an obtuse angle
might look like-- let me make it a little bit clearer. It might look like that. If this was a right
angle, this line over here would look something like that. It would be completely
upright relative to this if this were the ground. But we don't see that. This orange ray over here is
actually opened out wider. It's opened up wider. So it is obtuse. And this kind of comes from
the actual everyday meaning. Acute means very sharp
or very sensitive. Obtuse means not very sharp
or not very sensitive. So you could imagine this looks
like a sharp point or it's not opening up much, so maybe
it's more sensitive relative to other things,
or I don't know. I'm just trying to
make connections. This is less sensitive. It's all big and open. It won't be able
to notice things that are small
because I don't know. Maybe that's not an
appropriate analogy. But one way to think about it,
it's kind of open up wider, or it's bigger
than a right angle. It's larger than 90
degrees if you measure it. You would have to
rotate this ray more to get to this other ray
than you would if they were right angles, and
definitely a lot more than if they were acute angles. If I were to draw this with
lines, which of the angles are obtuse and which are acute? Well, the way I've drawn
them right over here, these two over here are acute,
and then these over here are going to be obtuse. This one and this one, these
are both obtuse angles. And I actually drew
it up here, as well. This one and this one
are going to be obtuse. So very simple idea. If one line or one ray
relative to the other one is straight up and down,
versus to left and right, or is completely
upright, then we're talking about a right angle. If they're closer to
each other, if you have to rotate them less, you're
talking about an acute angle. If you have to rotate
them more, you're talking about an obtuse angle. And I think when you just
look at them visually, it's pretty easy to pick out.