How to find angles formed when a transversal crosses parallel lines.

Hi everybody, welcome to my channel. So they say we should prove that you're a genius. But that's beside the point. This is what I saw in the question—we are asked to find the value. Of x, that is the question. Okay, so how do we go about this? This is what these three lines are. parallel to each other they are parallel to each other what does that mean means that no matter However far you draw them, they will never meet; okay, they can never meet now we have to find the value. Of x, let's get to it. First of all, we need to discuss the types of angles that are formed when you have a transversal drawn across two parallel lines; first of all, you are going to have vertically opposite angles; this is vertically opposite; this one is also vertically opposite to this, and what does the rule say? It says that they are equal. They are equal, which means if this If this is 20 degrees, this should be 20 degrees; if this is 100 degrees, this one should be 100 degrees. Okay, because they are vertically opposite, all right—the same thing applies to whatever is the same. This thing goes to this place, and this place, okay, this place and this place—they are vertical. opposite and they are equal, all right. Let's talk about the second type of angle that is formed. The second type that is formed is what if you have, um, something like this—they are called corresponding angles, whereby you see two angles occupying the same position they occupy the Same position. For example, notice that this is a parallel line; this one too is parallel. once you draw two parallel lines across each other, you will notice that This angle here is going to be complementary to this one because this is on at the top of your parallel line and on the left-hand side, okay, the same thing with this—this is also on top of your parallel line on the left side, so they are applying the same position They are corresponding and equal, so if this is 30 degrees, this should also be 30 degrees. Thirty degrees—the same thing with this side; if you have something like this and this They correspond; they'll find the same position, even this one here and this one here. They correspond; they are in the same position. Okay, all right, so that is corresponding. Angles. Now, let's talk about the third type of angle that is formed: um, what is the alternate? Angles—now this is the type of angle you form by drawing a Z. Okay, now look at this. If I draw a Z here, you're going to have an angle here, you're going to have an angle here. Right at the end of those pointed ends of that Z—this is what I drew. This one here is this. This one here is the notice that the pointed ends of this particular Z that I drew all the two angles formed there are alternate angles; if you have 20 degrees here, then this one It must not be something like this—your z must not be written like this, even if you write your z in the inverted form, which looks like this—even if you draw your z like this, it's something like like this, and like this—you're still going to get the alternate angles; this angle here will They are alternate angles, okay? So these are the three types of angles. There is another one, but It's not really necessary because I don't think we need this here; we don't need it here. So to cut our time short, let us apply these angles we have now. with us regarding this, and solve this problem, so let me switch what we have here First of all, you're going to notice that we already have vertically opposite angles. So this one is vertically opposite, which means this is 110 degrees. Okay, now if this place is 110 degrees, I want you to draw a z, an imaginary z, you are going to see what the The corresponding angle that is formed there; now let's draw the imaginary Z like this, like this. And just like this, you'll notice that this one and the entire thing will be an alternate angle, let me Draw it out—we have something like this, like this, and like this. Now this is our 110 degrees. This one is okay now. Remember that we have another line here. This is our 35 degrees, but the whole Of this, which is the other pointed end of our Z? It is 110 degrees, which means from here to here. It is 110 because they are what they are, alternate to this particular angle, so they are equal. I hope you're keeping up with me alright, so if this place is 110 degrees, then we can actually get Why, if you draw this line now, notice that we have this from here to here It's 110; let's call this place Y. If we call this place Y, I'm not going to clean this 110, so that This is what we have; we also have this angle here, from here to here, measuring 110 degrees, as well as this smaller one here. It's just 35 degrees, but from here to here it's 110—we're looking for this particular location now. Let's call it y; you notice that this one is going to be equal to this y plus the whole of This place, this is supposed to give us 180 degrees and continue in a straight line, okay? and go in a straight line, so it means that this y which we have plus the entire length of this from here to here, which is 110, is supposed to give us 180 degrees, right? So it means that our y is is going to be 180, and plus 110 will cross over to become minus 110, okay, so it means that our y becomes 70 degrees, so it means that this particular small portion here is now 70 degrees I want you to see it very well, so it means that this smaller portion is 170 degrees since from here to here is 110 degrees because it is alternate to this particular angle All right, now that you've got this, are you seeing what I'm seeing? I know you've seen it, okay, if This is the first time you're coming across my channel, so please I would like you to subscribe. to the channel so that you have access to my videos anytime I upload a new video, it will be notified, so I advise you to also click on the notification bell, okay? All right, now let me show. Why were you laughing? Our results are already out. Let me draw what we have. We have this here now, let me draw it. So this is what we have: this is the third parallel. Line, this is the x you are looking for now, from here to here. Now we have this, right? This one is And we have 70 degrees here; this 70, I'm drawing it out here so you can see it clearly. Now this is the x we are looking for. Can you see anything based on what I explained initially? Notice that this particular section from here to here is the same as from here to here. They are corresponding, okay. This is a parallel line. This is another parallel line. And we have a and this one is on the left side of the transverse, and this one is also on the left side of the transverse on top of our parallel line, so they're occupying similar The positions correspond, so this implies that our x is also equal to 35 plus 70. 35 plus 70, which gives us 105 degrees, and that becomes our answer. Thank you for watching. Have a lovely day, bye