The following VBA example initializes the snap points to which the dimension is attached and creates an angular dimension that is linked to the snap points. The dimension text is placed in the middle of the dimension arms, and then the vertex of the angular dimension is moved.
Sub Test()
Dim shp1 As Shape
Dim snpVer As New SnapPoint, snp1 As New SnapPoint, snp2 As New SnapPoint
'Initialize the snap points; this placement should form a 45 degree measurement.
snpVer.PositionX = 0.0
snpVer.PositionY = 0.0
snp1.PositionX = 10.0
snp1.PositionY = 0.0
snp2.PositionX = 10.0
snp2.PositionY = 10.0
Set shp1 = ActiveLayer.CreateAngularDimension(snpVer, snp1, snp2, 10.0, 5.0)
'Change the vertex of the angular dimension to coordinates (-10,-10); this should still form a 45 degree measurement.
shp1.Dimension.Angular.Center.PositionX = -10.0
shp1.Dimension.Angular.Center.PositionY = -10.0
End Sub