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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.
10 Ресурс 1 (1).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 \(180°\).
11 Ресурс 2.png
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 \(360°\).