How to find unknown angles in a cyclic quadrilateral.

Welcome to my channel. So we are asked to find the value of x in this particular diagram, okay. This is a very simple matter if you actually know the circle theorems that we are going to apply. Here, okay, so let's go ahead and do that. When you look at this question, now let me introduce you to cyclic quadrilateral: a cyclic quadrilateral is when you have a circle, okay, and you have a four-sided figure. figure inscribed inside the circle, not just that it's inscribed inside the circle, the four edges must be touching the circle for it to be a cyclic quadrilateral now there are certain um certain uh what is it called theorems that are involved in cyclic world one of them says that The opposite angles of a cyclic quadrilateral add up to 180 degrees; that means they are supplementary. So it means that if this is a and this is b, then a plus b, a plus b equals 180 degrees. So if this is a and this is b, then a plus b will give us 180 degrees; that is the first theorem. Okay, now the second theorem about cyclic quadrilaterals that we are going to apply to this says that the exterior angle of a cyclic quadrilateral, for example, if this is the exterior angle Okay, this particular place, if we call it x, states that it is equal to the opposite. interior angle, this is the opposite interior angle, let's call it y, so it says that x is equal to y Do you understand that this is the exterior angle, and this is the opposite interior angle, and both of these They are equal, so just watch how I'm going to apply this now to what we have on the board. Okay, looking at what you have on the board now Look closely and see if you can recognize one of those theorems I just taught you. Yes, notice that this is the exterior angle of this cyclic quadrilateral; this particular angle here. is the exterior of this cyclic world, so it means that this particular angle here, let's call it s Solution: So let's call it S. This S is equal to 92 degrees. This angle S is 92 degrees. Now, what is the reason? The reason is that the opposite exterior angle of a cyclic quadrilateral. The exterior angle of a cyclic quadrilateral is equal to the opposite interior angle. Okay, now I haven't gotten this. we have that the exterior angle is equal to the opposite interior angle, which means our s is what It's 92 degrees here, so if you look closely, you'll see what we have right now. Is something like this? This is the x you are looking for, right? This is 58, and this is what 92 that we got, and we are looking for x now. The answer is very, very close, but if this is the first when you come across this channel and have followed me to this level, it means that you Enjoy what I'm doing, and if you like what I'm doing, please click the subscription button. To subscribe, click the notification bell so you'll be notified whenever I upload. New videos, okay. All right, so look at this now. You know that the sum of angles in a triangle... It's supposed to give us 180 degrees, so that means 92 plus 58 plus x is supposed to give us 180. So 92 plus 58 will give us x plus 2 is 10, right? 0 carry 1, put it here to be 6. 6 plus 9 is 15. So I have 150, right? 150 plus x is equal to 180, and that means that our x is equal to 180. This plus 150 will cross over to become minus 150, so our x becomes equal to 180 minus 150. That will give us 30 degrees, and that is your final answer. Have a lovely day and bye.