 Hello friends welcome again to this session on lines and angles in the previous sessions. We Understood the meaning of lines angles. We also saw different types of angles and we also Learned how to measure angles. Isn't it now moving ahead? We are now are going to discuss what our complementary angles and Supplementary angles and other such definitions. So what are complementary angles now complementary angles are nothing but a pair of angles pair of Angles complementary angles are what pair of angles right whose measures whose measures some to Some to one right Angle Okay, this is what is called Supplementary angles. So for example, let us say we have angle theta and we have Angle phi right so theta plus phi is equal to 90 degrees or Pi by two Radiance in whichever unit want to see it so theta plus five must be equal to 90 degrees then we say And let let us also name them. So a b c and b q Are so hence we say angle a b c and Angle p q r Are complementary to each other are complementary Complementary Or we also say angle a b c is Compliment to Angle p q r Okay, the sum of the two angles must be 90 degrees now, let us try to You know a deep You know understand what the meaning why we why are we using the word complementary now? Complementary comes from the word Complementum Okay, it comes from the word Complementum What does complementing stands for so it's nothing but to fill up or to complete to Fill up so it is associated with the verb which means to fill up or to complete. Okay, so hence Hence you can understand now. What should be added it to? Angle to make it right angle is what is that meaning right so hence in other words You can say a complement is nothing but what is the complement of an angle? So the difference between difference difference between between an angle and Right angle is called Compliment of an angle difference between an angle and right angle. What does it mean? It means let's say you have 60 degrees So what should be added to 60 degrees to make 90 degrees? Clearly the answer is 30 degrees so we say 30 degrees is complement Compliment to 60 degrees, sorry 30 degrees complement to 60 degrees and vice versa Similarly, what should be added to 30 degrees to make it 90 degrees? You know, it is the answer is 60 degrees Right, so hence if you see if you want to find out the complement of 60 degrees What do you need to do you subtract that from 90 degrees so hence answer is 30 degrees Okay, so hence if Generalizing generalizing if theta or complement to theta complement To theta will be nothing but 90 degrees minus theta in degrees Is that okay? This is how you have to find out so hence Complement complementary angle of 45 degree is nothing but 90 degrees minus 45 degrees is equal to 45 degrees right complement of Compliment 245 degrees Is that fine? Similarly, if you have 53 degrees, let's say what is the complement of 53 degrees some complement of 53 degrees will be 90 degrees minus 53 degrees hence it is 37 degrees Okay, now, you know so hence To come complementary angles are nothing but a pair of angles whose sum is 90 degrees now Let us understand what are supplementary angles, right? So complementary angles are nothing but pair of angles whose sum was 90 degree right and one thing which I missed to tell you in complementary Angle was if you take an example, let's say if you have a right angle triangle If you have a light right angle triangle, so hence, let's say a B See and see is 90 degrees. Let's say then automatically a plus b angle a plus angle b is equal to 90 degrees by angle some property, you know, you know this Right, so angle a plus angle b will be 90, right if C is 90 that means in our right triangle right triangle in a right triangle the acute angles acute angles are complementary Complementary Okay, now look, let's have a look at supplementary angles. Now, let's say again, you have two angles angle a b c and Angle p q r. Okay, so a b c and p q r are called supplementary angles if Angle a b c plus Angle p q r is 180 degrees Okay, 180 degrees or by radiance Right, this is what is called supplementary angle. Now if they are, you know, if these two angles are adjacent That is if they have common Arm, let's say this is the common arm Right, so if you see if one arm is common, so this is theta This is let's say Phi Okay, so one arm is common. Let's say the name is p q r s Okay, so in in this case angle p q s plus angle P q r and that is equal to 180 degrees Okay, so in this case what will happen q s and q r are opposite rays opposite Raise now this this need not be all the time that means you can have separate angles as well for example This angle here is let's say Phi and This angle here another angle is here Which is theta they are two separate angles p q r. Let's say and a b c Okay, so they are also complementary if so angle p q r and Angle not not complimentary. Sorry supplementary angle a b c are supplementary supplementary if If Theta plus Phi is 180 degrees in this case. They are not adjacent angles if you see they don't share a common arm But in this case they share a common arm and in this this is a special case and which is called a linear pair linear pair Okay, so two angles Sharing a common arm and they two angles which are supplementary and sharing a common arm are is called linear pair Okay, now if you see s q r are co linear point so point s Q and r which lie here here and here they are co linear in that case right there that is they'll that is s R is a straight line Okay, so please keep in mind all these facts. So now let us take an example. So let's say what will be question is Let's say what is supplementary angle Supplementary Angle to 60 degrees So let that angle be x so let that Angle be x degrees So what do we know by the information we had about supplementary angle x plus 60 degrees is Equal to 180 degrees for supplementary so x will be equal to simply 180 degrees Minus 60 degrees Which is equal to 120 degrees Okay, so that's what is you know supplementary angle. Now, let's see in examples where We find Supplementary angles. So first example is in parallelogram. Okay, first example is parallelogram what happens in parallelogram adjacent angles in parallelogram in parallelograms adjacent adjacent angles are Always Supplementary, okay, what does it mean? So if you see there is a parallelogram here a B C D Now in this case alpha plus phi is equal to 180 degrees Similarly phi plus beta is 180 degrees Similarly beta plus theta is 180 degrees And theta plus alpha is 180 degrees all adjacent pair Are supplementary another such example is cyclic quadrilateral So we have a cycle the quadrilateral. What is a cyclic quadrilateral? Cyclic quadrilateral is nothing but a quadrilateral Who's all the vertices are on a? Circle, okay, so let's say a B C D Okay, a B C D are so a B C D is a a B C D is a cyclic Quadrilateral Okay, cyclic quadrilateral then angle a plus angle C is equal to 180 degrees opposite sum of opposite angles In a cyclic quadrilateral is always supplementary. Okay, and angle D so angle D Angle D Plus angle B is also sub 180 degrees. So hence we say opposite opposite Angles In a cyclic Quadrilateral quadrilateral are always Supplementary Okay, please bear these information in mind so that you can understand the properties of these geometrical elements in much better way Okay, so we will be dealing exhaustively about on on all these properties when we'll deal with let's say parallelograms and Cyclic quadrilateral. So now I hope you have understood. What is the meaning of? supplementary and complementary Angles now there's one more definition and that is something called angle bisector. What is angle bisector guys? Okay, so angle bisector is nothing but a ray which divides a given angle into two equal parts. So let's say this is one ray Another ray. So let's say this is a B C is an angle Okay, now angle bisector is nothing but a ray like BD Okay, such that BD is a ray BD is a ray Inside obviously inside the angle such that Such that Angle ABD is equal to angle C BD Okay, then BD is Angle bisector bisector of angle ABC Right, this is what is The definition. Okay, so other way to write this as is this angle ABD is equal to angle C BD is equal to half angle ABC half of ABC Is it okay? It bisects the angle into two parts So that is all about these angles and their you know attributes in this session