Theory:

Linear pair:
Linear pair of angles should add up to \(180°\).
 
If the given two adjacent angles does not make the \(180°\), then it is not a linear pair.
Angle.png
 
We studied that the sum of all the angles formed at a point on a straight line is \(180°\).
 
Think what would be the angle if many rays arises from a single point!
 
All the rays are starting from a single point. So the sum of the angles around a point will be \(360°\).
 
Now we understand this with some example.
 
Observe the below figure. Here \(AB\) is a straight line. And \(OC\) is a ray meeting \(AB\) at \(O\). It is evident that AOC and BOC is a linear pairs, so it makes the angles of \(180°\).
 
Screenshot 2020-10-15 143408.jpg
 
Also the another ray \(OD\) meeting \(AB\) at \(O\). Then AOD and BOD is a linear, which makes \(180°\).
 
We can observe that all the angles AOC, BOC, AOD and BOD are originated at the point of \(O\).
 
Therefore, (AOC+BOC)+(AOD+BOD)=180°+180°=360°.
 
Hence, it is clear that the sum of the angles at a point will be \(360°\).