 Hello friends welcome again to session on lines and angles and in this session We are going to discuss an interesting topic that is types of angles So I'm assuming you are you know sitting on the study table and there are lots of objects around you Okay, so if you are using our notebook to write the notes Then if you observe the two edges Adjacent edges of your notebook. They are meeting at a point and making an angle is it So look at the ceiling and the point where ceiling and a wall vertical wall is meeting again You can imagine or you can see there is an angle being made isn't it? So if you you know, basically the point is there are lots of You know angles around you which you observe on a daily basis But there are different varieties of angles as well So today in this session we are going to categorize those angles and hence the topic types of angles So this is how we categorize angles to start with so there is something called acute angle And how do we classify these angles on what basis and the basis is nothing but the angle measure So we measure the angle and if the angle is between 0 to 90 degrees we say the angle is acute angle We'll show you some examples with some pictures and all but right now Let's first go through the all the types and then we can see different examples, right now Right angle right angle is nothing but an angle which makes 90 degree So the angle between the two arms is 90 degrees called a right angle Okay, then there's something called obtuse angle guys obtuse means Something which is between 90 and 180 none of these two angles are included That is the angle must not be 90 and the angle must not be 180 degrees So anything between obtuse angle, sorry 90 and 180 is obtuse example 120 degrees 155 degrees and so on and so forth What is a straight angle straight angle is nothing but two arms if They are making 180 degrees, right? So hence this is the example of a straight angle So there's a point. This is point a b and c. So if you see this angle is 180 degree, right? It's called straight angle Then there's something called a flex angle again So if you see if you make an angle like that more than 180, but less than 360 is Reflex angle. Okay, and the last is complete angle that means the the two arm Coincide each other and hence this angle is called two six Complete angle and the measure is 360 degrees. I've also given the measures in radian for your understanding because later on we are going to use Radians a lot more than let's say degree So hence if you see a cute angle is nothing but between 0 to pi by 2 radian You must be remembering that 2 pi radian is equivalent to 360 degrees, isn't it? So 90 degree clearly will be pi by 2 radian. So 0 to pi by 2 radian is acute pi by 2 radian is right angle Pi by 2 till pi. So pi is equivalent to 180 degrees these radians So pi by 2 and pi are the limits for obtuse angle So the theta must be between pi by 2 and pi then straight angle, which is nothing but pi radian 180 degrees is pi radian and Reflex now, you know pi less than theta less than 2 pi radian is reflex because 2 pi is 360 And finally complete angle is 2 pi radians, right? So this is what is that different categories or different types of angles. Please keep these information in your mind Now, let us see some examples of these angles in our day-to-day life So here are few examples of acute angle if you see the edge of the knife, you know So it's very very small this angle this angle made at the edge is around 30 degrees. We see in this figure so this is an Example of acute angle Similarly the rockets if you see if I draw the you know the lines like that This angle has to be acute, isn't it? Similarly here also. These are all Angles acute angle. These are the you know practical application of acute angle So you're a rocket cannot have an obtuse angle like that You cannot have this the rocket will never have a shape like that. Why? because then the aerodynamics for the rocket, you know becomes You know poor and and and let's say it will it will face a lot of resistance from air while it is going up So basically whether it is a bullet or whether it is an arrow if you see we always have acute angles Because acute angles in such cases helps in you know Achieving the objective right so hence you see acute angles In such cases so here again another example is this cactus thorn if you see the thorn The angles are pretty Small isn't it? I'm not able to you know draw it so properly, but this is the case of acute angle Correct. So these are some practical applications or some examples where you see Acute angle now. Let us see some examples of other angles as well now here is an example of Or a picture of how about a bridge very famous how about a bridge in India? Okay, it's on the River Hoogley in you know and it it joins Kolkata to Havra. Yep. So hence this is River Hoogley Okay, so this is River Hoogley a distributory of Ganges Okay, so here is This bridge now here a lot of examples on different types of angles can be observed So let us first find out acute angles. So if you see very easily there are lots of acute angles guys This is one this is one like that, right? These are all acute angles. Can we get some 90 degrees or right angles? Yes, we have this is 190 degree. This is again another This one another this one another. So these are all perpendicular, right? So 90 degrees Similarly, if you see underneath also, there are lots of 90 degrees. Isn't it? These are right angles What about let's say The obtuse angle again. Yes, there are lots of obtuse angle as well How so if you take this arm and this arm so here there's an obtuse angle, isn't it? Similarly take this and this so this is obtuse Do we have some? Straight angles. Yes. So if you see this is the point. So this becomes the straight angle, right? So this is 180 degrees Two links are there like that 180 degrees straight angle. Okay, fair enough. Now. What about Reflex angle perfect. So we have reflex angles as well. So let's say this is one arm here and This is another arm here. So if you see this angle happens to be Reflex, isn't it? So if this is reflex automatically the other one is either obtuse or acute Okay, so this is a reflex angle now another example of reflex action Sorry, reflex angle would be so if you take let's say this arm and This arm so this angle is a reflex angle more than 180 degrees, but less than 360 and there are lots of examples of Complete angle. So let's say this is the point and hence You know, there are two or let me just give you this example Let's say this is one link one link is denoted by let's say this color. This is one link okay from here to here and Other link is nothing but from here only to this part So the angle between them is nothing but complete angle 360 degrees or Which is equal to zero degree as well Okay. So hence in one example in one bridge, you can see lots of different types of angles are visible Hope you understood the different types of angles guys Now does this mean that angles can be only till 360 degree? No, you can actually have 400 degree 400 degrees 560 degrees even 1 lakh degrees all is possible. Yeah, all are possible. But what does it mean? So for example, let's say this 400 degree 400 degrees nothing but imagine a line or ray Let's say this is point O and this is point P. Okay Now it starts rotating right it starts rotating anticlockwise and goes and goes and goes and comes back after some time back to the same position So hence we say it has covered a full circle or it has covered 360 degrees or two pi radians Okay, now if it moves ahead and let's say after crossing the initial point It is now somewhere here so that now it is making an extra 40 degrees angle So is the total angle if you see the total angle made by the line ray is nothing but 360 degrees plus 40 degrees which is equal to 400 degrees This is what is meant by an An angle which is having you know more than 360 degree value correct, so now you can see every 360 degree the The point or the ray will complete one cycle or one revolution Right one revolution one revolution so In 720 degrees it will cover to revolution It's like a you know a race which is happening and every 360 degrees one lap Okay, so hence. Yeah, so hence what will be one zero eight zero degrees. It is nothing but three revolution completed Okay, so hence now you can calculate what is one lakh degree as well and Any other value for that matter so hence degrees can also take values which are more than 360 Okay, so don't get confused when you see let's say tomorrow. They can say 520 degrees. So you now know 520 degrees means one full circle 360 and then another 160 degrees Is it so hence it is nothing but somewhere Here so hence it has the point has moved one full circle and in the second part It has gone to 160 degrees. Right. This is 160 degrees, right? So 360 plus 160 is 520 degrees. So then that is how you have to find out The meaning of all these numbers Okay, so we'll see you in the next class