UPSKILL MATH PLUS

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Learn moreLinear 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, $(\angle \mathit{AOC}+\angle \mathit{BOC})+(\angle \mathit{AOD}+\angle \mathit{BOD})=180\mathrm{\xb0}+180\mathrm{\xb0}=360\mathrm{\xb0}$.

**Hence, it is clear that the sum of the angles at a point will be**\(360°\).