Preferences | Alignment Angles

A line will automatically track to the angles input into the Alignment Angles snap field in Preferences.

Draw the first angled line from point 1 shown below, making sure the alignment tracks to 15° and connects with the projected intersection of the offset line, shown below as point 2.

Drawing the line at 15°

Repeat this for the other lines so that the result is shown below. Make sure all the lines track to a 15° alignment and connect to the offset lines.

All angled lines drawn at 15°