public Geometry Shape {get; set;}

// Modifies the geometry of an annotation feature in the specified annotation layer.
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(annotationLayer, objectId);
  //var shape = insp["SHAPE"] as Polygon;
  //...wrong shape...
  //Instead, we must use the AnnotationProperties
  //annotationLayer is ~your~ Annotation layer
  var insp = new Inspector();
  insp.Load(annotationLayer, objectId);
  AnnotationProperties annoProperties = insp.GetAnnotationProperties();
  var shape = annoProperties.Shape;
  if (shape.GeometryType != GeometryType.GeometryBag)
  {
    var newGeometry = GeometryEngine.Instance.Move(shape, 10, 10);
    annoProperties.Shape = newGeometry;
    insp.SetAnnotationProperties(annoProperties);
    EditOperation op = new EditOperation
    {
      Name = "Change annotation angle"
    };
    op.Modify(insp);
    if (!op.IsEmpty)
    {
      var result = op.Execute(); //Execute and ExecuteAsync will return true if the operation was successful and false if not
    }
  }
});