 This video is called Practice Problems 3. This is an excellent problem as it has many steps and requires that you know many things about angles and sides of a triangle. I recommend that you put a star next to this problem. It's something that you should study before your quizzes and your chapter 7 exam. So let's be careful and make sure that we answer, that we understand what's going on and we answer the question correctly. It says to list the sides, excuse me, let's try that again. It says to list the sides of triangle dgp in order from the longest to the shortest. But that's interesting. It's asking us about sides. Yes, it gives us information about angles. It says angle d is 9x plus 14. Angle g is 4x minus 2 and angle p is 3x minus 8. Well, if they give us information on angles, well, what do we know about them? The three angles of a triangle have to add up to 180 degrees. So let's see what happens when we do that. 9x plus 14 plus 4x minus 2 plus 3x minus 8 all have to equal 180 degrees. So now I just have a equation that I have to simplify and solve for x and that will help me. So let's go ahead and clean up this left-hand side. Combine like terms, 9x plus 4x plus 3x, 9 plus 4 is 13, plus 3 is 16. So I have 16x, then a 14 minus 2 minus 8. Well, 14 minus 2 is 12. 12 minus 8 is going to be, sorry about that. Let's try again. 14 minus 2 is 12. 12 minus 8 is going to give me a positive 4. So I have 16x plus 4 equals 180. I subtract 4 from both sides. So 16x gives me 176. When I divide both sides by 16, let's see, what do I get? X equals 11. So that's great that X equals 11, but my problem certainly isn't done yet because it didn't ask me to solve for X. I'm going to take a minute and make a sketch of my triangle. I don't know. Let's put D here, angle G here, and P here. And we have to figure out the sides from longest to shortest. Well, let's go ahead and plug in what we know about our angles. So angle D was 9x plus 14. So we'll do 9 times 11 plus 14. It gives me 99 plus 14, which is going to give me 113 degrees. So I know angle D is 113 degrees. All right, let's go ahead and do angle G. Angle G was represented by 4x minus 2. So I'll have 4 times 11 minus 2. 44 minus 2 is 42. So angle G was 42 degrees. All right, then lastly, angle P was, let's see, 3x minus 8. So you'll have 3 times 11 minus 8. Well, 3 times 11 is 33. 33 minus 8 is 25. So angle P is 25 degrees. All right, so that's great. So now I know that I could say, well, angle to list them from longest to shortest, angle D is longest, angle G is in the middle, and angle P is the shortest. Now many students would say that that is my final answer and you would get it wrong. Because you're absolutely correct that the angles from biggest to smallest would be D, G, and P. But the question was not asking that. It was asking you to list the sides from biggest to smallest. So let's look here. You might think, I don't know anything about the sides. I just know something about the angles. But the truth is you do. Remember, the largest angle, the side opposite will be the largest or the longest. The shortest angle, which in this case is P at 25 degrees, the side opposite that will be the shortest or the smallest. And then the angle that's in the middle, angle G, that's 42 degrees, well, the side opposite that will be the one in the middle. So I've got the longest, the shortest, and the medium or middle one you could say. So to list it from longest to shortest, well, my longest was G, P. My middle segment or medium segment was segment D, P. And my shortest was D, G. So that would be your correct answer. Not listing the angles, listing the side lengths. Be very, very careful when you do problems like this that you answer the question that's being asked. So if you look at your notes or look at the video, there's a lot up on the screen. We had to set up an equation. We set it equal to 180. We solved for X. I plugged my answer in to the three angles and found D, G, and P. And then it was really important that I made my little sketch or my little picture of my triangle so it made it very visually obvious to see which side was the longest, which side was the middle, which side was the shortest because you labeled D, G, and P with 1, 13, 42, and 25. So then you could get your answer correct. Good luck.