If the vertex is at the centre of the circle then this forms a sector of the circle.
If the two endpoints and the vertex form an angle in a segment, then the vertex can be at any point on the circle within the same segment and all angles so formed are equal.
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An angle has two endpoints and a single vertex.
Central Angle An angle in a circle with vertex at the circle's center.
An angle that's vertex is on the center of the circle.
inscribed angle
an angle in an circle whos vertex is on the circle.