Setting Map Distance Units to Degrees Minutes Seconds

I have a button in my Addin that changes the Data Frame display distance units to decimal degrees, which works well:

IMxDocument mxDoc = ArcMap.Document;
ESRI.ArcGIS.Carto.IActiveView activeView = mxDoc.ActiveView;
IPageLayout pageLayout = activeView as IPageLayout;
IMap map = activeView.FocusMap;
map.DistanceUnits = esriUnits.esriDecimalDegrees;

My problem is I would like to have a button that changes the map distance units to Degrees Minutes Seconds. I can do it manually through the Data Frame properties dialog box, but I am searching for a C#/ArcObjects way to do that.