 Hi folks, so we are back again with this problem solving session on straight lines and lines and angles So the problem given is two straight lines P Q and RS. You can see from the picture Intersect each other at O angle P O T pot P O T is 75 degrees. You have to find out the values of a B and C. Okay This is the question so Lots of straight lines things which come in them in in you know in our mind first of all is Vertically opposite angles and linear pairs and things like that. So we'll be using all this Insolving this question now clearly P Q and RS are Straight lines. So hence angle a is equal to 4 B. Why right vertically opposite angles Right a is equal to 4 B. Similarly, if you see 2 C is equal to 2 C is equal to B plus 75 degrees again Why because angle R or Q is equal to angle P O S Vertically vertically opposite angle. So this is relation number one. This is two Hence now one one more information you can see here is very easily a Plus 2 C is equal to 180 degrees. Why this is because of linear pair Right RS is the line and OQ is the ray on the line. So a plus 2 is 180 degrees So we got three relations and we know that three relations and how many variables three variables are there a B and C So now we can solve this. So now it is, you know only left to solve these equations Okay, so if you see you guys from two from How to solve now the art is how to solve. So hence can I replace? A and C A and C Let's say in terms of B. So what I'm trying to say is A is for B and C is this right so let's deploy a from here and and C into this Equation and then we'll get one equation in B. So if you see in the equation number three I can deploy the values of A and 2 C isn't it so from one for B plus 2 C is nothing but B plus 75 So this 2 C I am replacing by this part right and this a I am replacing with this part So 4 B plus B plus 75. So this was 2 C and this was a Is equal to 180 degrees Once again Instead of this a I am writing 4 B because a is equal to 4 B and instead of this 2 in in place of this 2 C I can write B plus 75. So I'm writing that here. So hence now why why does it? Why is it needed? How does it help? Because now I am getting an equation in only one variable that is B So hence 5 B Plus 75 is 180 degrees So 5 B will be equal to 180 degrees minus 75 degrees, which is 1 0 5 degrees Okay, so what will the value of B then so B is 1 0 5 degrees by 5 which is 21 degrees Okay, this method is called Substitution method of solving linear pair of our system of linear equation. Okay, so B is 21 degrees I got now B is 21 degrees. I can use one from one What is a? a is 4 B C equation number one here a is 4 B So this implies a is equal to 4 into 21 Which is equal to 84 degrees Okay, and from 2 2 C is equal to B plus 75 degrees Right, this implies 2 C is equal to B B was 21 degrees plus 75 degrees Okay, which is equal to 96 degrees. So what is C then C will be 96 degrees upon 2 which is 48 degrees Isn't it so this is what we have Got so a b and c all three values. We could figure out a is What is a? a is equal to where is a so this is 20 B is 21 a is 84 and C is 48 degrees so hence the problem is solved. So what is the learning again learning is use of vertically opposite angles and Linear pair using that we framed three equation and then it was reduced to solving the linear Equations to get the final results