Here's how you can automate this with arcpy geometry objects:
>>> import math
>>> length = 100000
>>> lines = []
>>> degrees = 5
>>> with arcpy.da.SearchCursor("YOUR_POINT_LAYER_NAME_HERE","SHAPE@") as cursor:
... for row in cursor:
... for i in range(360/degrees):
... dx = math.cos(math.radians(i*degrees))*length
... dy = math.sin(math.radians(i*degrees))*length
... startPoint = row[0].centroid
... endPoint = arcpy.Point(row[0].centroid.X+dx,row[0].centroid.Y+dy)
... line = arcpy.Polyline(arcpy.Array([startPoint,endPoint]))
... lines.append(line)
...
>>> arcpy.CopyFeatures_management(lines,'in_memory\lines')
edit: I just read the point about limiting between 180 and 360. This can be incorporated into the above script.