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# Acute, right, & obtuse angles

CCSS.Math:

## 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 our acute angles acute angles right angles right angles and obtuse and obtuse angles and I think when we just go through these it'll be pretty self-explanatory an acute angle is an angle well let me just draw them first then you might you might 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 I could also so the acute angle will be this angle right over here I can 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 we're going to see as acute angles or ones that are with accents I haven't defined right angles yet they're narrower and 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 complete I don't want to use the word right in my definition but they're kind of if one is going horizontal the other one will be going vertical so let me draw it with Ray's 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 the general convention for labeling right angles is to put a little kind of a half of a box right over there and that tells me that that is a right that means that that is a right angle or that if this is going left to right this is going perfectly top-to-bottom that there that this is in no way kind of it's completely I guess the best way to think about 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 is that this angle is its opening is smaller it's more narrow it's it's a it's a the 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 an obtuse angle might look like let me make it a little bit clearer might look like that if this was a right angle this this line over here would be would look something like that it would be completely upright relative to this if this were the ground but we don't see we don't see that this orange ray over here is actually opened out wider it's opened up wider so it is obtuse 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 could imagine this looks like a sharp point or it's it's it's not opening up much so maybe it's more sensitive to you know 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 they won't be able to notice things that are small because I don't know and maybe maybe that's not an appropriate analogy but one way to think about it it's kind of opened up wider or it's bigger than a right angle its larger than 90 degrees larger than 90 degrees if you measure it you would have to rotate this rate more to get to that to to get to this other way than you would if they were right angles and definitely a lot more than if they were acute angles I were to draw this with lines 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 are acute and then these over here are going to be obtuse this one and this one these are both these are both obtuse angles and I actually drew it up here as well this one and this one are going to be AB obtuse so very simple idea if if one if one line or one ray relative to the other one is straight up-and-down versus the left and right or it's completely upright then we're talking about a right angle if they are 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 we need to just look at them visually it's pretty easy to pick out