Everyone, let's use what we know about angles to 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 rough. They don't have to be perfect. Let's take a look at the first one, which is 45 degrees. What does that look like? Well, let's 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 in this first quadrant over here. What does 45 look like? Well, if you 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 draw it so that it is perfectly at the northeast, upright corner, and I'm basically just cutting these two angles in half like this. That would be 45 degrees. Alright? That's about what that would look like.

Let's look at the next one here, which is 210 degrees. Again, let's use our axes as guides. This is 90, and this is going to be 180. 210 is bigger than 180, so you're going to start to go around in this direction into this third quadrant, because this is going to be 270, that's too big. So it’s going to be somewhere over here. So if you look at the halfway points between 180 and 270, something like this is actually 225. You can figure that out just by taking the difference between those. So that’s too big as well. 210 is going to be somewhere over here. Let’s use what we know about 0 and 30, to 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 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 basically this, which is in the third quadrant. So all that really means here is you can take this line at 30, and you can kind of just imagine that it extends 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 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.

Now let’s look at the last one over here, which is negative 100 degrees. 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. 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 flip numbers. Right? So this is 270, but this would be about what negative 90 degrees would look like. Remember, these are right angles. This would be 180, but also it would be negative 180 if you go around a little bit extra. So if you were going in the clock- wise direction, you would go past 90 and then a bit extra, like 10 degrees. What happens is I'm going to draw a line that looks like this. So this is a full 90 degrees in the negative direction, but then it's a little bit extra. So this angle, which we draw clockwise, would be negative 100 degrees. 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.

Let me know if you have any questions. Thanks for watching.