public MapPoint Centroid( 
   Geometry geometry
)

{
  // simple polygon
  List<Coordinate2D> list2D =
  [
    new Coordinate2D(0, 0),
    new Coordinate2D(0, 2),
    new Coordinate2D(2, 2),
    new Coordinate2D(2, 0),
  ];

  polygon = PolygonBuilderEx.CreatePolygon(list2D, SpatialReferences.WGS84);

  // verify it is simple
  bool isSimple = GeometryEngine.Instance.IsSimpleAsFeature(polygon);
  // find the centroid
  MapPoint centroid = GeometryEngine.Instance.Centroid(polygon);
  // centroid.X = 1
  // centroid.Y = 1

  // map Point
  MapPoint pt1 = MapPointBuilderEx.CreateMapPoint(1, 2, 3, 4, SpatialReferences.WGS84);
  MapPoint pt2 = MapPointBuilderEx.CreateMapPoint(5, 2, double.NaN, 7);

  // pt1.HasZ = true
  // pt1.HasM = true
  centroid = GeometryEngine.Instance.Centroid(pt1);
  // centroid.HasZ = true
  // centroid.HasM = true
  // pt1.IsEqual(centroid) = true

  // multipoint
  List<MapPoint> list = [pt1, pt2];
  Multipoint multipoint = MultipointBuilderEx.CreateMultipoint(list);
  // multipoint.HasZ = true
  // multipoint.HasM = true

  centroid = GeometryEngine.Instance.Centroid(multipoint);
  // centroid.X = 3
  // centroid.Y = 2
  // centroid.HasZ = false
  // centroid.HasM = false
}

{
  var oid = 1; //ObjectID of the annotation feature to modify
               // Note: QueuedTask is required to access the AnnotationFeature
  {
    //Don't use 'Shape'....Shape is the bounding box of the annotation text. This is NOT what you want...
    //
    //var insp = new Inspector();
    //insp.Load(annotationLayer, oid);
    //var shape = insp["SHAPE"] as Polygon;
    //...wrong shape...

    //Instead, we must get the TextGraphic from the anno feature.
    //The TextGraphic shape will be the anno baseline...
    QueryFilter qf = new QueryFilter()
    {
      WhereClause = "OBJECTID = 1"
    };

    //annotationLayer is ~your~ Annotation layer

    using var rowCursor = annotationLayer.Search(qf);
    if (rowCursor.MoveNext())
    {
      using (var annoFeature = rowCursor.Current as
      ArcGIS.Core.Data.Mapping.AnnotationFeature)
      {
        var graphic = annoFeature.GetGraphic();
        var textGraphic = graphic as CIMTextGraphic;
        var textLine = textGraphic.Shape as Polyline;
        // rotate the shape 90 degrees
        var origin = GeometryEngine.Instance.Centroid(textLine);
        Geometry rotatedPolyline = GeometryEngine.Instance.Rotate(textLine, origin, System.Math.PI / 2);
        //Move the line 5 "units" in the x and y direction
        //GeometryEngine.Instance.Move(textLine, 5, 5);

        EditOperation op = new EditOperation();
        op.Name = "Change annotation angle";
        op.Modify(annotationLayer, oid, rotatedPolyline);
        op.Execute();
      }
    }
  }
}