 This video is called Sol for X using parallel lines and a transversal. The instructions for this video say Sol for X in each problem below. State the theorem or rule that you applied to help Sol for X. Also show the equation that you created. So basically we want you to show your work by setting up an equation. Don't just give us the answer for X. So looking at this first problem, I see that I have two horizontal lines and they have the parallel marks on them so I know that they're parallel. So that would make this third line going in the opposite direction, the one that's more up and down, my transversal. So to look at this picture, to Sol for X, X is on the inside of my parallel lines and it's on the left side of the transversal. 51 is also inside my parallel lines and on the left side of the transversal. So what kind of angle pair is that when they're on the same side of the transversal and inside the parallel lines, that makes them consecutive interior angles which in the previous video we decided that consecutive interior angles are supplementary. And remember, it should be fairly obvious not to say that these two are equal because if you just looked at them and tried to be logical about it, this X angle is bigger than 90 degrees so it's obtuse. This angle up here is less than 90 degrees so it's acute. They do not look equal so you wouldn't set them equal. So even if you forget their name, if you forget that they're consecutive interior, you should be able to look at the picture and say, nope, they're not equal so I'm going to choose the other kind and say their supplementary. So our equation will be X plus 51 equals 180 because that's what it means to be supplementary. The two angles add up to equal 180. So to Sol for X, I subtract 51 from both sides and I get X to be 129. So that is our example number 13. On to example number 14, we have another picture where I can see that my horizontal lines are parallel. I know that because this time they both have the double arrow. This is maybe the first time we've seen the double arrow. I know they're parallel because they both have two arrows with them just like you've seen before them both having one arrow. So then my transversal must be the vertical line going up and down. Now before we pick out our theorem and write our equation, let's go ahead and just think about this for a second. My X looks like it's on the left side of the transversal, outside or on the exterior of my parallel line. The 94 is on the other side of the transversal, the right side, and it is also on the exterior or outside of my parallel lines. So what relationship are they when they are on alternate sides of the transversal and outside of the parallel lines? If you're thinking alternate exterior, you were right. And then hopefully you took good notes from the last video and you can remember that alternate exterior angles are congruent. Now if you forget all of that, again just try to be logical about it. This angle looks just a titch more than 90 degrees and so does this one looks a titch more than 90. They can't be supplementary so they must be congruent. So in this case if they're congruent you just set the two things equal to each other. X equals 94. And in this case there's nothing to solve. We solved it. X equals 94 so you already have your answer. This video. This last video, again, start before you pick out your theorem. Just look at the picture. I've got parallel lines that are horizontal. I know that because of the parallel arrow marks. The transversal is cutting through. And then take a look. The 105 degrees is on the right hand side of my transversal and underneath the parallel line. The expression 2x plus 1 is on the left side of the transversal and it's above my, or inside the parallel line. So they're on alternate sides of the transversal inside the parallel lines. So that makes them alternate interior angles. And if you remember from the last video, alternate interior angles are congruent. Again, just try to be logical about it. They're both obtuse. So you know they're both more than 90 so they can't add, if you added them up they'd be more than 180 degrees. So you're not going to call them supplementary. They look like they're congruent and they are. So we'll set them equal to each other. Sorry. We have 2x plus 1 equals 105. So I subtract the 1 and get 2x to equal 104. And when I divide both sides by 2, x is 52. So my answer for this is 52. This concludes the video. Solve for x using parallel lines and a transversal.