 Welcome friends to another problem solving on lines and angles. I hope you are going through the previous video sessions as well to get a proper understanding of the concepts and different types of problems. So let's solve this problem given in this. So lines x, y and mn intersect. So you can see there are two lines x, y and mn, x, y and mn they intersect at point o and it's given that p, o, y so this angle is 90 degrees okay and a is to b so this angle is a and this angle is b here so a is to b is 2, 2 is to 3 and you have to find out c okay. So again the moment I see 90 degrees and you know ray op stands on line x, y or you know so we get a you know the first thing which comes to your mind is you can use linear pair over here. So let's start the solution okay what's given let's first write down given so you have to write that angle p, o, y is equal to 90 degrees and a by b is 2 by 3 right this is given right now we don't really mention those which are pretty obvious for example mn being the line and x, y being a line you can write that too okay so you have to find what c okay so how to find that now a by b is equal to 2 by 3 this implies what does it imply a is equal to 2 upon 3b many people start with saying a or calling a as 2x and b as 3x and then solving you can do that or this so hence I use this this method so a is 2 by 3b because it saves me another variable anyways so now angle p, o, x and angle p, o, y form a linear pair so angle p, o, x and p, o, y form a linear pair what does that mean it means angle p, o, x plus angle p, o, y plus angle p, o, y is 180 degrees that is what we have learned right now p, o, x can be clearly written as a plus b isn't it if you see a plus b gives you p, o, x and p, o, y was 90 degrees right so this is equal to 180 degrees so now what a plus b is 180 degrees minus 90 degrees is equal to 90 degrees okay now a plus b is 90 degrees so and we also know that a is 2 by 3b so put it as 1 so using 1 using 1 in 2 what is 2 so let us put this as 2 using 1 in 2 what will you get you will get a as 2 by 3b so let's write 2 by 3b in place of a so I am writing 2 by 3b right this a is replaced by 2 by 3b because of this and then plus b is 90 degrees 180 minus 90 is 90 so now that means taking LCM you will get 5 by 3b is equal to 90 degrees so this implies b will be equal to 90 degrees into 3 by 5 isn't it so hence this is nothing but 72 degrees I am sorry 54 degrees okay why because 5 this is 5 so 5 18 so 54 degrees okay the moment you got b you can find a okay now basically you just wanted b why now only b can help you finding c okay now if you see in this figure b plus c is again 180 degrees why linear pair okay so you can write here b plus c is 180 degrees why you can again write linear pair that means c is equal to 180 degrees minus b which is equal to 180 degrees minus 54 degrees which is nothing but 126 degrees this is what it is the value of c so hence what is the learning from this problem guys so the moment some information is given you know what information was given 90 degrees was given and then a and b ratio was given and lots of straight lines you could see and you know that in a straight line the total angle is 180 degrees linear pair right so using that concept and the given information we could convert the problem into algebraic equations and we solved equations to form to find the given value that was c in this case I hope you understood how to solve these kind of problems