Two straight lines can be met at a point on a plane and the meeting of them causes the formation of an angle at their meeting point.
Hence, the meeting point of any two lines which form an angle is called vertex of the angle.
Consider two lines and assume their endpoints are meet at a point on the plane.
An angle is formed geometrically due to the meeting of the endpoints of the both lines and the point is known as vertex of the angle.
The vertex of the angle is a point. So, the way the point is represented in geometry and the same way the vertex of the angle is also denoted in geometry.
The point is denoted by uppercase alphabets. So, the vertex of the angle is also represented by the same uppercase alphabets.
In this example, the meeting point of the both lines is called as point $E$. Therefore, the point $E$ is also known as the vertex of the angle.