How to find Angles formed by a transversal across parallel lines.

Hey guys, you're welcome to my channel. We are asked to find z, like this angle here. What is the value? When nothing is given to us, like there's no number here, let me come outside and you'll see. There is no figure here, nothing, and we have to find the value of z. How do you go about it? Okay. Follow me, let's do this together. First of all, we're looking for z. The first thing we need If you draw this particular triangle, this is a triangle, right? This is a triangle, xz. And yes, this is a triangle, and the sum of the angles in a triangle will give us 180, right? so that brings us to the first thing we need to write here; here it says that the first thing we need Yes, this is our solution. The first thing we need to write is that z x plus y equals 180 degrees; what is our reason for the angle in a triangle? Somehow finding a the triangle will give us 180 degrees, okay, we have that number one, we are looking for the The value of z is given to us by this p q and s r; this arrow indicates that both of them are parallel. What does parallel mean? It means that no matter how far you draw them, they can never come together. Okay, they can never cross each other; they will keep moving away from each other, so if you are When I give you this kind of thing, parallel lines, I usually tell you people that there are several angles that are formed when a transversal crosses a parallel line, because if I should Extend this parallel; we keep going like this, and there is a transverse here. The line I'm seeing here is a transverse. This line is also a transverse. Okay, let me show you what. I mean, if you have two parallel lines like this, just like we have here, and you have a transversal Just like you have this line, okay, several angles are formed: number one of them is or maybe I should just talk about the one that we are going to encounter here, so let Let me talk about the alternate angles formed when two parallel lines are crossed by a transversal. Now when you talk about an alternate angle, you're going to visualize a Z in your mind, a Z like this. When you form a Z, see what I did—the angles you have at the tip of your Z are your alternate angles. The angles you have at the tip of your Z are alternate angles, and they are equal. That means if we have 20 degrees here, it's also 20 degrees here—do you get me? Okay now. Let's use this thing I just explained here to relate it to what we have here, okay? First of all When you have this kind of situation, draw another parallel line—that's what I tell my students. draw another parallel line to intersect it at this point, okay? So this line is also parallel if it is Like this, you can now see that your transverse will be very easy to obtain by looking at this now. You're going to see that two Zs are formed; you're going to see this one like this, like this. and like this, that is the first one, so here is our x; it means that you know, from here to Here is our z, but it means that by the time we form this z like this, see the z we form like this, this place is x, which means the upper part of this place is also x, which means we have Here to be x, are you getting me? See the z we formed like this, so it means that this upper Part is also x, so we have established that. Here is x. Now look at me again and see another z that is formed that is going to show us that we are forming another alternate angle, so we are going to have it like this, one two three, so you're going to have this now, this particular place is Here, right, and this is y; this is y, which means this place is also y because our z is also From there, so what is this showing us? It means that this x plus this y will give us this z. Everything here is z, so this x plus this y will give us this z. Okay, so let's go ahead and write that now. The second equation we found is that x plus y is equal to what are you okay if you've followed me to this level, to this stage, it means that you are actually enjoying what I'm doing, so I think it's time for you to hit that subscription button Okay, please subscribe if you haven't already, and also hit the like button and turn on your notification bell. So I'll be notified anytime I upload a new video, all right? Okay, now we have found this. If we should substitute, let's call this equation one, okay, and call this equation two. then substitute z equal to x plus y into equation one, substitute z, that is, this z equal to x plus y in equation one—what does that mean? It means that in this equation one Anyway, I see z; I'm going to put x plus y, okay? So I'll now write x plus y, which is this z here. plus x plus y x plus y equals 180 degrees, okay. Now, x plus y plus x plus y, if we should Collect like terms. Collect like terms. We are going to have that x plus x will give us what? 2x plus y plus y gives us 2y equals 180 degrees. Okay, now 2x plus 2y, if we factor out These two will have two brackets: x plus y is equal to 180 degrees. Now, how do we get it? our x plus y, we divide both sides by two, right? If we divide both sides by two, we are going to We cancel these two, divide them by themselves, one divided by 180, we are going to get 90 degrees. So we now have that x plus y is equal to 90 degrees. Now let me shock you—we have that what x plus y equals 90 degrees right now. Notice that our x plus y equals z, so what is it? telling us that it means that therefore our z is equal to 90 degrees And that is your answer. Do have a lovely day and bye.