 Okay, so more questions to solve now in this question to supplementary angles are in the ratio 2 is to 3 Find the angles so you have to Find the angles which are supplementary and the ratio is 2 is to 3 how to do it. So let us say the angles are Angles are X and Y so don't you know hesitate to take as many variables as Possible and later on once you are very adept at it. You will be able to do it By minimizing the number of variables as well. So for the start. Let us take the angles to be X and Y Now what information is given first of all? They are saying the angles are supplementary in nature. That means what first information I have to convert it into an equation So this first information is two supplementary angles. That means X plus Y is 180 degrees first information Name the equation as 1 label it as 1 now second information is the ratio is 2 by 3. That means X upon Y is 2 by 3 So by manipulating you can write X equals to 2 by 3 Y Okay, this is let's say relation number 2 now Using 1 and 2 now let's use both 1 and 2 together. What does it mean? So substitute? Y or X and the first Equation so X plus Y was 180. So now we got X is this much. So I can write 2 by 3 Y instead of X. So instead of this X. I'm writing 2 by 3 Y Y Because of this relation plus Y is equal to 180 degrees, isn't it? Now you can take Y common So Y common 2 by 3 plus 1 Equals 180 degrees. So which is nothing but Y and you can take the LCM and you'll get Y 5 by 3. Okay is 180 degrees So this implies Y is equal to 3 upon 5 into 180 degrees Okay, so 5 3 and 6 36 times 5 is 180 so hence this answer is Nothing, but 1 0 8 degrees Okay, so Y is 1 0 8. What would be X then simply X is 2 by 3 Y Which is nothing but 2 by 3 into 1 0 8 degrees. How do I know this? I know this because of this relationship, right? So hence the answer is 2 by 3 into so 3 is 36 and this is nothing but 72 degrees. So the answer is the solution to this question is 108 degrees and 72 degrees. Let's see another question. Now in this question It says the complement of an angle Compliment of an angle. So the moment this is there, what does what comes to your mind first? So complement of an angle is nothing but let us say the angle is Theta or again, if you don't like theta, let's put it as X. So let's say the angle is X Okay, now again the complement of an angle is one-third of itself. So So complement of an angle. So what is complement of an angle? So I'm just converting the language English into mathematics to complement. Sorry, sorry for the bad spelling complement complement of X will be nothing but 90 minus X Isn't it because X plus 90 minus X here if you see X plus 90 minus X added together gives you 90 degrees Is it it since complement is nothing but 90 minus X. So what is what does it say? It says Compliment is one-third of itself. Okay, so what is complement 90 minus X? so complement and Then there is a word is which means equal to in mathematics then one third is nothing but 1 by 3 off means multiplication and Itself what was itself X? So this is the equation. Okay, so you need just need to solve this So 90 equals X upon 3 plus X if you take this X on that side So 90 is equal to 4 by 3 X right after taking LCM. So hence X is 90 into 3 upon 4 Which is nothing but for if you do this calculation this 22.5 base. So hence it is nothing but 67.5 Degrees right. So that is one That is let's say X. So this is angle X. Sorry to mind the angle. So X is 67.5 0.5 degrees. So what is complement of X? 90 minus X which is 90 minus 90 degrees minus 67.5 degrees, which is nothing but 22.5 degrees Okay, so you see these are the two solutions two values So one angle is 67.5 and one third of it anyways is 22.5 and if you add both of them this plus this you will get 90 degrees. This is what the question was all about Okay, so I hope you understood how to solve such questions you