Hello all!

I am attempting a project that tracks the lunar cycle in a circular map, which looks like a pie chart. The problem I'm having is that "Lunar months" are not a nice even number. For instance the Lunar month of August 2018 is 29 days, 8 hours, and 4 minutes. If it were just a round 29 days that would be easy, but I'm having trouble accounting for the extra third-ish of a day.

What I'm trying to devise is a circular map with spokes radiating from the center, creating triangle slices that consist of a lunar day. Therefore, 29 of these equal length days, but then a proportionally small 8hour and 4 minute slice. I'd like to do one of these for each month and the number of additional hours and minutes changes pretty dramatically so I was hoping someone could show me a methodology to calculate this myself for the future. I won't lie, I'm pretty uneducated. I've been using adobe Illustrator which has a great tool for this assuming your numbers are nice and round. I can simply enter into the rotation box 360/29 and get nice even slices. But this takes up the whole circle. I need 29 even slices PLUS the extra bit.

If anyone is willing to help me with this I would be very appreciative. Thank you just the same for taking the time to read my request for help!