Can I do this in draw?
In principle it works. Draw a circle. If you need angle measurements, you need 360 short dashes. The strokes set and position each stroke in the correct angle. Depending on the accuracy you need, the circle should be as large as possible. You can e.g. specify a page format of 1 m x 1 m and make the circle correspondingly large.
You can also buy a transparent circle ruler. They are usually available for 180 degrees. Scan the circle ruler, copy it and put it together as a circle.
Your question should be more detailled…
Quick and dirty: Create a pie chart in Calc, then insert in Draw. There you have to break it.
Example: Have a column with 10 times number 30 in it. Create the pie chart, insert data labels (30), copy and paste into Draw as LibreObject. Select the chart, right mouse handle, break.
Apply/Add a dashed line and edit size and spaces. So degrees can be simulated.
[EDIT]It is even possible to draw a circle (only line), define the dashed line (as seen above) and to count the single “degrees”. Scaling the size of the entire circle and/or editing size and spaces of the dashes can alter the amount of the “degrees”.[/EDIT]
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Other possibility (for advanced use) is the DMaths extension (English tutorial available).