 So now that we've gone over some of the vocabulary of a circle, we're going to just do a couple of practice problems. So in number one, we are given circle C and we are told that the measure of angle A, C, B is 21x minus 7. So this angle right here is 21x minus 7. And we are told that the measure of angle B, C, D, which is this angle right here, is 5x plus 5. What we want to do is we want to be able to find x and then plug that back in so that we can find the measure of angle B, C, D. Well, what we have to recognize here is that we are looking at the diameter, A, D, which is cutting the circle in half. Well, that means that the measure of angles A, C, B, and B, C, D, if you add those together, it should equal 180 degrees. So what we're going to do is we're going to take 21x minus 7, add that to 5x plus 5, and set that equal to 180. So now let's just solve this for x. If we combine like terms, if I had my marker on here, 21x plus 5x is 26x. Negative 7 plus 5 is minus 2. And so then we're going to add 2 to both sides. We get 182. And if we divide both sides by 26, we get x equals 7. Once we know that x equals 7, we can go ahead and plug that back in. In this case, we want to find the measure of angle B, C, D. So the measure of angle B, C, D, since B, C, D is 5x plus 5, we're going to do 5 times 7, which is 35. Add 5 to that and we get 40 degrees. So the measure of angle B, C, D would be a 40 degree angle. Number two, find the diameter and circumference of a circle with a radius of seven units to the nearest tenth. So here's our circle. We know that radius is the measure from the center of the circle out to a point on the circle. If that's seven units, then in order to find the diameter, we would just double that. So diameter is equal to 2 times the radius. So in this case, the diameter is 14 units. We'll just use U for units. And then the circumference we talked about, there's two ways to find circumference. We can either do pi times diameter or we can do 2 times pi times r. Well, we know both of those distances. We know the diameter is 14. We know the radius is 7. So I'm going to just go ahead and plug 14 in for D and the circumference would be 14 pi units. Now, this did ask us to find it to the nearest tenth. So here's where you would use your calculator and we are estimating 14 times pi. Your calculator should have a pi button on it. And when you multiply 14 times that pi button, you get 43.982. Well, if we round to the nearest tenth, 43.98 actually would round all the way up to 44 units because 43.98, you can't round a nine up. So we would round up to 44. Number three, we are given the diameter of circle L and circle M are 20 and 13 units respectfully. What that means is that the diameter of circle L, so P r is 20 and the diameter of circle M, which is QS is 13. I'm going to just for, from those two pieces of information, I'm also going to then identify that the radius, so P L and R L are both 10 in circle L and the radius Q M and S M would be 6.5 for circle M and one other thing they tell us is that Q R is 4 and what we want to do is figure out L Q and R M. So first thing I'm going to start with is right here Q M is a radius of this circle and right down here, we just identified that Q M is 6.5. Well, if this is 4 and the whole thing is 6.5, then that means R M, sorry, R M would have to equal 6.5 minus 4, which is not 1.5. If you do the math, Ms. Davidson, 6.5 minus 4 would be 2.5. So R M, this little piece right here, would have to be 2.5. The other piece that we want to find is L Q. So once again, I'm going to just remind remind everybody that L R is the radius and we found down here that R L is 10. So if this whole thing is 10 and Q R is 4, we can figure out L Q once again by using subtraction. Oh no. Sorry about that. Let's see where was I. So L Q would have to be L R, which is 10, subtract this little piece of 4. So L Q would have to equal 6. So this piece right here is 6. In this problem, we are asked to find the exact circumference. Now when it says that word exact, it means that you're going to leave your answer in terms of pi. You're not going to put it into your calculator and multiply it out. So we know that circumference is equal to pi times diameter. And if I look at this picture, this is the diameter. So if I can find D, I'll be able to find the exact circumference. So what you have to recognize is that we are working with a special right triangle. What you notice here and here is that these are both legs equal to 5 and this is a 90 degree angle, which means we're dealing with a 45 90 triangle. And so if the legs are both 5, then that means that the diameter has to be 5 root 2. I now can plug that in pi times 5 root 2. And because it wanted the exact circumference, what you're going to do and how you're going to write your answer is 5 pi root 2. And that would be considered the exact answer.