 alright friends so having seen the theory part now it's time to solve some problems because this is the only way you learn mathematics so let's start first question says find the measure of an angle which forms a pair of supplementary angles with itself okay so you have to find obviously you have to find something there's a question so you have to find something out measure of so you have to find what measure of n what angle okay so that means you have to find an angle x so that's how we start which forms a pair of which forms that means x forms a pair of supplementary angle with itself okay so that means x is doing something with itself and it is forming a pair of supplementary angle so what is it doing basically so that means you know some of two angles is 180 degrees then they are called supplementary angles so x with itself is forming supplementary angles that means x plus x must be equal to 180 degrees so that means 2x is equal to 180 degrees so what is x guys x is 90 degrees so remember learning what's the learning learning is a right angle right angle is supplementary to itself right supplement of itself or rather we write supplement of itself why because if you add right angle to a right angle we'll get 180 degrees understood that's how you solve the problem next let's go to second problem now this problem says two supplementary angles differ by 34 degrees find the angles okay so information let's mine the data it says two supplementary angles so there are two angles okay two angles so we start with this itself let the angles be angles be theta and phi if you are not comfortable with theta and phi you can say x and y so let us take x and y only instead of theta and phi because you guys are more comfortable I believe in let's say x and y now mind you x and y are the angle measures not the angle itself okay now what they differ by 34 degrees okay so they differ means x minus y is 34 degrees that's what they are saying and I would find out the angles so there could be lots of possibilities okay so what could be x and y so x is 35 let's say x is 35 and y is 1 so you see what is the x minus y x minus 5 will be 34 so will this be solution can you say that x is 35 and y is 1 or for that matter 36 and 2 this is also 34 or 37 and 3 this is also 34 so in all the cases you are getting 34 so what which one will you take up obviously there is one more information and that is the angles are supplementary what did we learn so supplementary means x plus y is 180 degrees so this also has to be satisfied now unfortunately 35 plus 1 is 36 so if you see x plus y is it working it is 36 it is 38 I'm sorry yeah 38 and this is 40 so none of them are working so hence you have to keep on doing to get x plus y is 180 but then we also have another smart ways of solving this what do you do is add both of them both these equations yep so adding equation means add LHS to LHS RHS to RHS what will you get you will get x minus y plus x plus y is equal to 34 plus 180 okay now if you know how to solve a pair of linear equation nothing like it otherwise you can substitute also so hence your y gets cancelled so you get 2x is equal to 214 180 plus 34 is to 14 so x my dear friends what is x then so x is 214 by 2 so hence it is 107 degrees isn't it 107 degrees so what will be the other angle other angle you can use any of these equations so hence x is 107 so deploy 107 minus y is 34 so what is y y will be 107 107 minus 34 degrees which is equal to 73 degrees isn't it and have you got the right answer we can check so the other equation was x plus y other equation was x plus y is equal to 180 degrees let's check whether it is satisfying or not so x was now what was x x was a 07 so 107 degrees plus y what was y 73 degrees add them up you will get 180 degrees so that means our result is correct so x is 73 uh x is uh sorry 107 and y is 73 so we got the results correctly so this is how you have to solve these kind of problems