Cyclic Quadrilateral. How to get angles in a cyclic quadrilateral.

Everyone, we are asked to find the lettered angles in the diagram below. That means you have to find the angle between vectors a, b, and c. Let's get into it. Okay, first of all, this The particular question is under cyclic quadrilateral: what is a cyclic quadrilateral? A cyclic quadrilateral is what when you have a circle and you have a quadrature, which is a four-sided figure inscribed within that circle, meaning the circle that particular diagram—that is what I have that it is a cyclic quadrilateral, and there are some theorems associated with this cyclic quadrilateral. quad Okay, then one of them is this, one of them is that—the sum of opposite angles of a cyclic a quadrilateral is 180 degrees; what it means is that if you have a here and you have b here, it means that Okay, now let's relate this to what we have here. When you look at what we have here now. you are going to notice that the area you are looking for is opposite this 80-degree mark, so that means That solution, so what does it mean that a this a you have here plus this 80 degrees is supposed to To give you 180 degrees, okay, based on what I told you, the reason was the sum of the opposite angles. sum of opposite angles of a cyclic quadrilateral is 180 degrees, which means our angle a is equal to to 180 minus 80, which is 100 degrees. Okay, we have been able to find what our A is to get the Now, if we apply the same theorem, we will be able to find x, because x is opposite to what it is opposite to. This 60, okay, so let's do the same: x plus 60. This x plus this 60 is supposed to give us what? 180. degrees right, the reason being the same thing: the sum of opposite angles of a cyclic quadrilateral is just write the same thing now we have got that means that our x is equal to 180 minus 60 which is 120 equal to 120 degrees, okay, we have obtained our x to be 120 degrees, we can now find our b Right, how can we get our B? You know, this is what we have here—we have something like this. This is our B degrees, and this is our X, and we have found our X to be 120 degrees. if x is 120 degrees, we can easily determine b because the sum of angles on a straight line is what 180 degrees, so it means that this 120 plus b is supposed to give us 180 degrees, so we are going to do what we are going to use it to find the value of our b, so we are going to write that b plus x equals 180 degrees, what is the sum of the angles on a straight line? angles on a straight line, sum of angles on a straight line—that is what I wrote inside Bracket all right, we have gotten, we are looking for B plus, we have gotten our X to be what, 120 is equal to 180, which means that our b is 180 minus 120, which will give us 60 degrees. Okay, so we have Got everything. The only thing that's left now is this, but before I continue, if you Having watched this far means you enjoy what I'm doing—please click subscribe. button so that you'll be seeing more of this, okay, and the notification bell so that you'll be Notified anytime I upload a new video. All right, let us continue. We have gotten our b to be 60. Degrees. Now we are looking for CC, which is the only one remaining, but I want you to look at this diagram. Just look at this— you know that if I remove this circle now, I'll see a triangle. If I remove this... Circle and this center line, I'll have a triangle. This triangle is what I'm going to have something. Like this: this is the C, this is 60, this is angle A degrees—that is without this, and the circle. So it means we can easily find our angle C because the sum of the angles in a triangle is 180. and we've already got our A up to 100, so if we have 100 here and 60 here, we can We can easily get our C because the sum of the angles in a triangle is supposed to be 180 degrees. So I can now write that this 60 here, 60 plus this a here, plus this c here, is equal to 180 degrees. The reason is that the sum of the angles in a triangle is 180 degrees—just know that that's what it is. Inside that place, the sum of the angles in a triangle—that's what's inside there, all right. We have 60 plus what is our A? Our A is 100. 100 plus C, which we are looking for, is equal to 180. Degrees, I think I can now clean this diagram; it's of no use anymore. All right, 60 plus 100. is going to give us 160 plus c equals 180, okay? That means our c is worth 20. This will cross over to become minus 160, okay, so it means that c is equal to 118 minus 160. Your c is equal to 20 degrees, so we have gotten our a to be 100, our b to be 60, our c to be 20 degrees, and our x to Be 120 degrees, you have a lovely day and bye