 All right, friends welcome again to another session on lines and angles in the previous session. We discussed about measurement of an angle is it it we discussed about measurement angle measurement measurement of an angle and We discussed three ways of Measuring an angle one was sex idea symbol the other one was centesimal and The most commonly used is the circular measure measure that is in radiance So but one thing which I missed out in you know the last session to tell you is that one in in sex are decimal system where angles are measured in degrees this was the conversion so one degree is equal to 60 seconds Sorry 60 minutes Okay, 60 minutes 60 minutes And it is also denoted as 60 and then this sign here 60 minutes. Okay, and one minute One minute is equal to 60 seconds and it is given my double dash. Okay, so 60 seconds 60 seconds, so please keep in mind so for example if I have three degree And then it's usually written as three degree 20 minutes and 35 seconds that means this is three degrees so Total number of seconds if you if you see what is the total number of seconds here is nothing but three in 260 in 260 plus 20 in 260 Plus 35 these many seconds are there. Okay, right? So in one minute, how many seconds are there 3600 seconds are there 60 times 60. Okay, this is what was not discussed in the last class so if you see in geography when you discuss about latitude and latitude and longitude so actually we measure The angles to this precision right so degrees minutes and seconds. There's a Application of it. Another thing is the concept of negative angle So there is negative angle is also possible negative angle While measuring we might have negative angle. What does it mean? So the convention says if you are measuring the angle in anti-clockwise direction So if you're measuring from positive axis in anti-clockwise direction, then this is considered to be positive angle Okay, while if you are measuring in Clockwise direction from positive x-axis then it is Negative angle so angles can be negative as a less positive and we will see the application the application is quite large in let's say areas of trigonometry and other such Application areas. Okay, so hence, please remember though theta is positive or angle is positive if you measure in anti-clockwise direction Anti-clockwise direction is considered to be positive Okay, and clockwise direction clockwise direction Is considered to be negative Okay, so please keep this thing in mind now. Let's talk about Actions related to angle and the first action is congruent angle measure action What does it mean and what does axioms mean basically so axioms are nothing but facts mathematical facts Uh, which are established and they did not have any proofs as such Okay, so they are established facts which are you know Which are not dependent on any proofs So congruent angle measure axiom says that two angles are congruent If they have same measure that means if you have two angles here If you see angle abc is equal to angle pqr if the measure is same Then they are called congruent angles Similarly, if they are congruent Then their measures will be same. So this is what is You know expressed by congruent angle measure Action right so two angles are congruent if they have the same measure and vice versa That means if two angles are having same measure measure means if they have same degrees or radians then the two Angles are congruent. This is congruent angle measure action Now the second action says angle addition action. And what is this? Let's say you have a point p in the interior of the In the interior region of the angle, right? There's a point p here Now point p if you join B and angle abc is the given angle and you are joining point bp points bp Then angle addition action says that angle abc will be equal to angle abp plus angle pbc That means theta plus phi is equal to angle abc, right? So hence for example, if you have let's say 15 degree here and let's say this is 90 degree here So the total angle will be nothing but 90 plus 15, which is 105 degrees Okay, this is what angle action angle addition action says the third angle is angle construction action And what does it mean? It says that if there is a ray ab An angle of same measure can always be Constructed on either sides of ab that means if you see here is a Line ab ray ab and I have drawn another ray ab such that angle a angle p ab is theta And I've drawn another ray aq like that such that angle q ab is phi And it happens to be that theta is equal to phi Okay, so hence I can draw same measure angle on both sides of a given ray. That's another action and that's called angle construction action I hope the three actions are clear to you and the concept of negative angle and The conversion between degree minutes and seconds Okay, so we'll meet you in the next session