 Hi, I'm Zor. Welcome to Unisortification. Today we will continue with basic concepts of geometry. We will talk about angles. Well, basically angle is a geometrical figure which is formed by two rays. Or if you wish two segments, doesn't really matter, which have common vertex. So this is called vertex and these are sides, sometimes legs of the angle. Now, Angles can be of different kinds basically, but what's very important is to understand how to measure them. Here is the process which basically helps to understand what is the measurement of the angle. So these are two rays and first we will consider that these two rays coincide basically. So one and another are on top of each other. It's obviously to call this angle measured as zero of something. Now the unit of measurement is at degree and now we will start rotating one of these two rays counterclockwise. And this will be the positive direction of increasing the value of an angle. Now, whenever this ray reaches the position which is the continuation of the first ray, so they actually make a straight line together because each ray is half-line. So if these two rays form one straight line, we are saying that this is an angle of 180 degrees and whenever we go further, another 180 degrees. Obviously, the full angle is 360 degrees. This is by definition. You don't have to basically have any kind of an explanation. We just decided that the entire full angle is 360 degrees and half of it is a hundred and eighty. So obviously the quarter of this angle which is a perpendicular is 90 degrees. Now there are other measurements of the angles. Well, actually one other measurement of the angle, called ray-gen. But we will talk about this a little later. We will talk about circles. But right now, let's just agree about the degrees as measurements of the angle. So we have right angle, which is 90 degrees. Right angle. And then we have half a circle, which is a hundred and eighty, and the full circle or full angle, which is 380. Now the angle which is less than 90 degrees is called the cute. So this is 90 degrees. Less than 90 degrees is called the cute. Angles greater than 90 degrees but less than a hundred and eighty degrees. Are called obtuse. So this is obtusable. This is 90 degrees. This is greater than 90 degrees. If two angles together, this one and this one, make 90 degrees angle, the right angle, it's called complementary. So angle A plus angle B equals 90 degrees it's complementary. Complimentary. Now if two angles make a hundred and eighty degrees, this one and this one, one is, let's say, a cute angle and another obtuse, or if you wish, which is the same thing, one is the right angle and the other is the right angle. Both together, they still make a hundred and eighty. So these two angles are called supplementary. Supplementary. OK. Now, what's very important is to understand that the measurement of the angle goes counterclockwise. So if you have an angle like this, what's its measurement? Well, you start from this position and go counterclockwise. And this will be, let's say, I know it's greater than 90, obviously, let's say it's a hundred and twenty degrees. Well, at the same time, you can measure from this ray again counterclockwise and it will be 360 minus 120, this is 240 degrees. So these are two different angles. So how can we say which angle do we mean in this particular case? If one ray is OA and another is OB, we actually have to know from which to start. So if we start from OA and move counterclockwise, we have a hundred and eighty, a hundred and forty degree angle. But if we start from OB and go to OA, it will be 240 counterclockwise again. So when we are talking about angles, we usually specify using notation like this. This is the sign of an angle. Now, AOB means the start from the end A or from the ray OA and go to the OB, which is the receiving side, so to speak. So the primary is OA and the secondary is OB. We move from OA to OB and this angle is this one. So as it is in this picture, AOB is a hundred and twenty degree and BOA is two hundred and forty degree. So we have to really understand what exactly is happening in this particular case and which particular angle is more important or less important. And you basically decide based on what exactly you want from your drawing and which angle you really need. Alright, so basically that's about it for angles. Angles do actually correspond to one of the main fundamental points which we have, like points and lines. Angle is just the next in the level of complexity, geometrical figure after lines and after points. We will probably use it, we will definitely use it in more complex geometrical figures like triangles, polygons, squares or whatever else. So this is basically what exactly the angle is and how to measure this angle. That's it. All the combinations of angles and lines which make up geometrical figures we will consider in the next lectures. Thank you very much. That would be it for today.