Hi Doris,
If you just click on the snap-to-angle button, QuiltAssistant should snap to angles in steps of 15 degrees, or whichever setting you chose earlier for your project.
To choose a specific angle, use to drop-down menu by clicking on the small triangle to the right of the button:
The closest to 60 degrees in the list would be 30. Alternatively, you can click on 'Custom...'. With that, a dialog will appear where you can set the exact angles you want at the bottom. The small square shows a preview of the angles you selected. For 60 degrees, you would want a "Step" of 60 and a "Base angle" of either 0 or 30 in most cases.
Hope that helps,
Arnout