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.

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 $\angle \mathit{AOC}$ and $\angle \mathit{BOC}$ is a linear pairs, so it makes the angles of $$180°$$.

Also the another ray $$OD$$ meeting $$AB$$ at $$O$$. Then $\angle \mathit{AOD}$ and $\angle \mathit{BOD}$ is a linear, which makes $$180°$$.

We can observe that all the angles $\angle \mathit{AOC}$, $\angle \mathit{BOC}$, $\angle \mathit{AOD}$ and $\angle \mathit{BOD}$ are originated at the point of $$O$$.

Therefore, $\left(\angle \mathit{AOC}+\angle \mathit{BOC}\right)+\left(\angle \mathit{AOD}+\angle \mathit{BOD}\right)=180\mathrm{°}+180\mathrm{°}=360\mathrm{°}$.

Hence, it is clear that the sum of the angles at a point will be $$360°$$.