 Okay, so this first practice problem says a regular hexagon is inscribed in a circle for a logo. So this, we're pretending this is some company that has a logo. Remember that hexagon means that we have six sides and it says opposite vertices are connected by the line segments, so that just means that here's a vertex and it's connected to the opposite vertex. What is the measure of one central angle? And so you can see in the picture x represents one central angle. So in order to do this problem what we have to remember is that all central angles in a circle add up to 360 degrees. So if I were to start here and go all the way around the circle and end up back where I started, that would be equal to 360 degrees. Because this is a regular hexagon, it means that all six sides are congruent, which means all six interior angles are also congruent. What it also means, because this is inscribed in a circle, it means that all six of the central angles, so this angle, this angle, this angle, this angle, this angle, and this angle, all of those angles have to add up to 360 degrees. So again, because we have six of them and we know they have to add up to 360, we can just take 360 divided by 6 and know that one central angle is going to be equal to 60 degrees. This is a problem that we are being introduced to in this chapter, but we'll actually come back and use in future chapters, so keep this in mind. Okay, for the second problem here we are going to use the theorems that we just talked about in the previous video. So what we're looking at here is circle W and we can see that it's been named by its center point of W. This circle has a radius of 10. Now what I want you to notice is right now, how this circle is drawn, there is not, well I guess I'm lying, there is a radius drawn, but notice it's not hj. If you're going to label the radius, you have to make sure you go from the center. So we're going to label MW as 10 and also, I'm not going to put it on the picture, but I'm also going to just write a note to myself that WL is also 10, okay? So WM and WL are both equal to 10 centimeters. Now the other thing we notice here is that WL is perpendicular to HK and that's theorem number two that we just talked about in the previous video, so I'm going to go ahead and mark this and then it tells us that HK is 16. Well remember that if these, if the diameter is perpendicular to the cord, remember what we said about the cords. So if HK is 16, that means that JK and JH are congruent. So I'm over here, I'm going to also write down that h, oops, hj has to be equal to 8 because if HK, the whole thing is 16, then hj has to be 8 and kj has to be 8. Okay, so let's see what part A is asking us to do. If the measure of arc HL is 53 degrees, we want to find the measure of arc MK, alright? So what that means, if HL has a measure of 53 degrees, this arc is 53 degrees, remember what the theorem told us, this arc KL would also have to be 53 degrees. Now if you remember back to 10, 1, and 10, 2, the other thing we know is that MWL creates a semi-circle, so arc MKL has to equal 180 degrees. So we might write that down, that the measure of arc MKL has to equal 180 degrees. So if we want to find MK, that's this angle, or this arc right here, oops, MK is this arc right here. Well if I know that the whole arc, the whole semi-circle is 180 degrees and LK is 53 degrees, then the measure of arc MK would equal 180 degrees minus that 53 degree arc. And so we get 127 degrees for arc MK. So that's the answer to part A. Okay, part B. Now part B wants us to find WJ. WJ is this little piece right here. Well what we have to do in order to find WJ is we have to think about the information that we do have. Remember before we said that KJ was 8. Okay, so I know that this is 8. Also remember that back in the beginning of number 2, it said that the radius of the circle is 10. Well not only is MW and LW a radius, but so is WK. WK is a radius because it goes from the center to a point on the circle. So I'm going to label that with the radius of 10 and I'm going to label this with 8 which is what we found out earlier. And now because of this right angle, I can use Pythagorean Theorem to find WJ because I have a right triangle. So I'm going to move my page down here a little bit and I'm going to set up A squared plus 8 squared equals 10 squared. And if we go ahead and solve this for A, A squared plus 64 equals 100. We subtract 64. A squared equals 36. We figure out that A is 6. So therefore WJ is 6.