 In this video, Practice Problems 2, we're given some information regarding this diagram. So let's go through and see what we're told here. Triangle TBU right here and TSU are both inscribed in circle P. You'll notice that one of the sides of each of those triangles is the diameter, so we know right away that we're dealing with right triangles that we'll mark in a second. We're also told that arc VU is congruent to arc SU. This is arc VU, this is arc SU, so I'm going to go ahead and mark up some stuff based on this first line of given information. If I know that those arcs are equal, I'm just going to put congruency marks there to remind me of that, and I know that these are each right triangles, so I'm going to mark that up as well, and that will help us to find our missing measures here. I'm asked to find the measure of each numbered angle, so I need to find the measure of angle 1, angle 2, angle 3, and 4 separately. I'm told that the measure of angle 2 is x plus 9, so I'm going to write that down right here, and then the measure of angle 4 is 2x plus 6. So it's a good idea to mark up your diagram with all the given information and then we can see where we're going to start. I have information about every angle in my triangle TSU here, and I know that for a triangle, all the angle measures need to add up to 180 degrees, so x plus 9 plus 2x plus 6 plus the 90 degree right angle have to equal 180 degrees. So there's my first equation. I'm going to go ahead and combine like terms and solve for x here. I get 3x equals 75, so I found out that x equals 25. I can't stop here because I'm asked to find the measure of each numbered angle, so now that I know that x equals 25, I can go ahead and plug that in for angle 4 and angle 2 to start out with, and I get 2 times 25 is 50 plus 6, 56 degrees. That's the measure of angle 4, and I'm going to circle that because we're going to have a lot of information on here, and then I'm going to do the same thing for angle 2 here. x plus 9 becomes 25 plus 9, so the measure of angle 2 equals 34 degrees. So I found the measure of angle 4 and the measure of angle 2. Now we need to go ahead and figure out what angle 3 and angle 1's measures are, and that's why it's important to put in that given information from the beginning. If these two arcs are equal, arc VU and arc US, that means the inscribed angles that intercept those arcs are also equal. So if VU and US are equal, that means angle 1 is going to be equal to the measure of angle 2. So I already found the measure of angle 2 is 34 degrees, so I know that the measure of angle 1 is also 34 degrees, and I have to write out each of these angle measures. And the other thing I know that if the two arcs VU and US are equal, then these arcs VT and ST are also equal because each of these is a semicircle, so that's what's left over on my circle. So that tells me that angle 3 has to be equal to angle 4 as well. So if angle 4 is 56 degrees, then the measure of angle 3 is also 56 degrees.