How to divide a binary image into different segment and put it as different binary image?

Hi, I'm new to Matlab, I have a binary image (find attached 'binary mask.fig' file) that I want to segment it into 4 segments. Each segments have their specific angles. Segment 1 should be the region I selected using ginput (find attached 'Ginput segment 1.fig' at segment 1) and the rest of the segments are:

Segment 2: 30 degree after segment 1, Segment 4: 30 degree after segment 3, Segment 3: is the rest of the remaining angles,

The segmented mask should be something like in 'Examples of segments.fig'

Any help would be appreciated thanks.