The letter E would be at the vertex. The two lines enclosing the angle E would be ED and EF. Usually, to make it quite clear we would call angle E by the description "angle DEF or angle FED (they are the same angle).
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the vertex of the angle is the point
vertex angle
The vertex angle is connected to the vertex point
If the 58°-angle is one of the base angles, then the vertex angle is 64°.If the 58°-angle is the vertex angle, then the vertex angle is 58°.
Yes, as long as the label for the vertex stays in the middle, you can read it in any direction you want.