public MapPoint Centroid( 
   Geometry geometry
)

// simple polygon
List<Coordinate2D> list2D = new List<Coordinate2D>();
list2D.Add(new Coordinate2D(0, 0));
list2D.Add(new Coordinate2D(0, 2));
list2D.Add(new Coordinate2D(2, 2));
list2D.Add(new Coordinate2D(2, 0));

Polygon 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 = new List<MapPoint>() { 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

      await QueuedTask.Run(() =>
      {
          //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(annoLayer, 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...
          //At 2.1 the only way to retrieve this textLine is to obtain the TextGraphic from the AnnotationFeature
          QueryFilter qf = new QueryFilter()
          {
              WhereClause = "OBJECTID = 1"
          };

  //annoLayer is ~your~ Annotation layer

  using (var rowCursor = annoLayer.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(annoLayer, oid, rotatedPolyline);
        op.Execute();
      }
    }
  }
});