 Hello friends Once again, I'm back with another question on lines and angles now in the given questions given that x plus y is Equal to w plus z you have to prove that aob is a line Aob is a line. Okay, so how to go about it now x plus y is equal to y plus z Now always remember if someone is asking you to prove aob to be a line What do you what do you think the basic concept should be so aob is a line That means any point on the line will make a 180 degrees. So for example, if this is a line So if you take any point here the angle around it will be 180 degrees. Is it it angle around it will be 180 degrees Okay, so this is what The concept of a line suggests so now so I have a point here Oh, if somehow I prove that x plus y or z plus w either of them is 180 degrees Then my problem is solved. So hence we'll start with Given okay, so what's given given is x plus y is equal to w plus z Okay, and you have to prove to prove that aob is a line or angle aob aob Is equal to 180 degrees. This is what you have to prove aob is 180 degrees. How to prove So solution so how to do so you know that x plus y plus w plus z is equal to 360 degrees Isn't it? Why is it? because angle around the point angle around the point adds up to 360 degrees This is what is our knowledge Okay, so now x plus y was equal to w plus z. Isn't it? So hence from here if you see x plus y was w plus z So hence I can write this as x plus y and instead of w plus z I can again I can again write x plus y Because x plus y was equal to double plus that and this is equal to 360 degrees Okay, so hence I can write two times x plus y is equal to 360 degrees So what will be x plus y simply? 360 degrees upon 2 which is equal to 180 degrees Okay, so hence I mean what is x and y? Friends if you see x plus y is nothing but angle aob Okay, so hence I can write angle aob is equal to 180 degrees hence My dear friends a b is a straight Line why because oa and obr opposite race is that clear? This is how you have to Solve this problem. So the learning is That if you have to prove that something is a line Then you have to prove that if you put any pick any point on that line a total angle made Will be 180 degrees. Okay, and hence you can prove that Given line or given geometric element is a line. Thank you