A point where an angle is made by the intersection of two lines, is called vertex of an angle.

$\overrightarrow{PQ}$ and $\overrightarrow{PR}$ are two lines and they both meet each other at their common point $P$.

The intersection of the rays $\overrightarrow{PQ}$ and $\overrightarrow{PR}$ formed an angle at point $P$. The point is the only reason for forming the angle between them. Therefore, the point $P$ is called vertex of the angle.

So, every point where an angle is made by the intersection of the lines, is known as vertex of the angle.

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