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.
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#
snpVer.PositionY = 0#
snp1.PositionX = 10#
snp1.PositionY = 0#
snp2.PositionX = 10#
snp2.PositionY = 10#
Set shp1 = ActiveLayer.CreateAngularDimension(snpVer, snp1, snp2, 10#, 5#)
MsgBox shp1.Dimension.Angular.TextX
MsgBox shp1.Dimension.Angular.TextY
End Sub