Everyone, let's use what we know about angles to go ahead and work out this example. We're going to draw and sketch each of these angles in standard position. They're just sketches, so they can be kind of rough. They don't have to be perfect. Let's go and take a look at the first one, which is 45 degrees. What does that look like? Well, let's just use our axes as guides for this because we know this is 0, we know this is 90, this is 180, and 270. So 45 is going to be somewhere between 0 and 90. It's going to be somewhere in this first quadrant over here. What does 45 look like? Well, if you actually think about it, 45 is exactly halfway between 0 and 90. That's exactly what 90 divided by 2 is. So if I were to grab a line and start to sweep it out towards the 90-degree angle, I would stop basically at halfway which is almost like a perfectly diagonal line like this. That's what 45 degrees looks like. So, I'm just going to take a line and I'm going to sort of draw it so that I'm going to be, like, perfectly at the northeast, you know, upright corner, and I'm basically just going to be cutting these two angles in half like this. So, this would be 45 degrees. Alright? That's about what that would look like.

Alright, let's look at the next one here, which is 210 degrees. Alright? So 210. Again, let's use our axes as guides. This is 90, and this is going to be a 180. 210 is bigger than 180, so you're going to start to go around in this direction over here into this 3rd quadrant because this is going to be 270, that's too big. So it's going to be somewhere over here. Alright? So if you look at halfway between 180 and 270, pulling it halfway like this is actually 225. You can figure that out just by taking the difference between those. Alright? So that's actually too big as well. 210 is going to be somewhere over here. It's going to be somewhere in this area. So let's use what we know about 0 and 30, to sort of draw this. Because if you look at this, the difference between 180 and 210 is 30 degrees. So what does 30 look like in the first quadrant? Well, if you draw this out, it's going to look something like this. Right? That's about what a 30-degree angle looks like. So the difference between 0 and 30 is this. So if you go halfway around the circle to 180, the difference between 180 and 210 is also what this is, which is in the 3rd quadrant. So all that means here is you can take this line at 30, and you can kind of just imagine that it keeps extending out in this direction over here. I'm just going to extend the line, because now that angle is going to be 30 degrees from a 180 degrees. Right? So this is going to get me 210 over here. It's 30 degrees from 180, but if you go all the way around the circle, that whole angle over there is 210 degrees. Hopefully, that made sense. Alright?

Now let's look at the last one over here, which is negative 100 degrees. Alright? So remember, these first two have been both positive numbers, so we've been going counterclockwise. Now we're actually going to go in the clockwise direction, the same way that the clock goes because it's a negative angle. Alright? So, and because it's rolling in the negative direction, our axes won't help us so much because we know this is 0, 90, 180, and 270, but we don't know what these negative angles are. Well, what happens is, if you just go around in the other direction, you sort of just flip numbers. Right? So this is 270, but this would be about what negative 90 degrees would look like. Remember, these are right angles. Right? This would be a 180, but it would also be negative 180 if you go around just a little bit extra. So if you were going in the clockwise direction, you would go past 90 and then a little bit extra, like 10 degrees. Right? So this line, which we draw clockwise, would be negative 100 degrees. Right? It's about what that would look like. Again, these are sketches. They don't have to be perfect, but, hopefully, you got something that looks like this. Alright? Let me know if you have any questions. Thanks for watching.