How to solve cyclic quadrilateral in circle geometry of maths.

Welcome to my channel. This is a cyclic quadrilateral. Okay, so we are asked to find the angles indicated by the letters. What does that mean? We are asked to find our m, our n, our k, and our p. Okay, that sounds so ambiguous, but don't worry. I'm going to give you the answers step by step in a way that you'll understand. Okay, let's do this. First of all, we need to know some things about cyclic quadrilaterals. What does cyclic mean? Quadrature means a quadrature, which is a four-sided figure inscribed within a circle, a cyclic quadrilateral. First of all, we need to know some circle theorems before we can begin this. One of the circle theorems states that angles in the same segment are equal. Angles in the same segment are equal. What does that mean? If you have a circle like this and you have a chord This is a chord, which is a line segment that divides a circle into two parts. But not into two equal parts. It states that when this line cuts the circle We are going to have two segments. This is the main segment. the major segment And this is the minor segment That is the large one, the major segment. The last one is the minor segment. Okay, now there's this law that states that any angle, all the angles on the major segment or on any segments They are equal once they are in the same segment. So what does that mean? It means that If we have this It means that as far as I am concerned, I have this These two angles here. This is a and this is b, notice. They start at a and end at b, right? If you have a and you have b, it means that a is equal to b. Because they are on the same segment on the same segment That is essentially the same on the main segment as what we have here, something like this. And we have something like this, any angle we have here will be equal to any angle. We are going to have them there because two of them are also inside the same segment. Now let us apply that to what pertains to what we have here. Now let's use it to evaluate what we have here as you look at this picture. We're going to see that we have a chord here, right? Then we have a line drawn from this point; let's call it a and b. Draw from this a to this b. Okay, and another line drawn from this a to this b, and we have this and this. So it means that this 60 and this m are in the same segment, so we can say That m is equal to 60 degrees. Why? Angles in the same segment, okay angles in the same segment Okay, we are able to get the value of our m as what 60 If we have our m to be 60, see this and this, see this end, see this 100. They are on a straight line. We have something like this day. This is our m This is our n, and this is 100 degrees. Okay Now there is another rule that states the sum of angles on a straight line is 180 degrees. What does that mean? It means that when you add m and n and 100 degrees, you're supposed to get 180 degrees. Alright, so I've been able to establish the fact that our m is 60 degrees. so to obtain our n, we can say that 60 degrees, which is our m right plus our n plus 100 What is supposed to give us 180 degrees? Okay. Now we are going to have 60 plus 100, which is going to give us 160. So we have 160 plus n equals 180 degrees. That means our n is equal to 180 minus 160 Let me write it here So it means that our n is equal to 180 minus 160, which is 20. degrees Okay, we have obtained our m and we have obtained our n. Now, what do we do again? Okay There is another law in the cyclic quadratic theorem, and that law states that The exterior angle of a cyclic quadrilateral Is equal to the opposite interior angle Don't worry. I'll explain if this is a circle. I have a quadrature that is something like this. A square is a four-sided figure. I have an exterior angle. This is what the exterior angle is. Let's call the exterior angle angle a, this a, okay, and there's another opposite interior angle. Now this is the interior angle. Let's call the interior angle b, which is opposite to this a. The law is telling us that this a is equal to this b, that a is equal to b. I hope you've seen this clearly, because I'm going to clean it now. Due to the limited space now, let us relate it to this. This external angle of this cyclic quadrilateral 100 is opposite to this p. You can see that, so it means that this p is equal to what? 100 degrees, and what is the reason I just gave to you, so we can write We can write that p What is equal to 100 degrees, and what is the reason? Exterior angle exterior angle of A cyclic quadrilateral is equal to the opposite interior angle. angle Okay, haven't gotten that yet. We can obtain our k as usual. How do we obtain our k? I would like you to do that and give me the answer in the comment section using the segment. I taught you in the initial sign. Alright, have a lovely day and bye.