I have several line text-files of (used in GMT) saved in the format (this is a small sample):

-111.29 42.28
-111.29 42.31
-111.29 42.33
>
-111.37 41.99
-111.38 42.02

I am trying to convert this to a Shapefile to use in QGIS. I know people convert from shp to GMT with ogr2ogr can you do this in reverse GMT to Shp? I tried using ogr2ogr and had no luck. Maybe I did something wrong or it is not possible with that tool.

I have tried to import this format in QGIS via the delimited text layer tool, but can only figure out how to get points when I need lines.