There's a way using a PowerPoint VBA Macro, as all shape objects can be manipulated from there.
Below is some sample code that asks for the starting and finishing angle, and creates a partial circle shape sized accordingly.
Dim startAngle As Double, finishAngle As Double
'Ask the user for values for Start and Finish angles
startAngle = -InputBox("Select the starting angle (relative to the x-axis, counterclockwise)", "Start Angle")
finishAngle = -InputBox("Select the finishing angle (relative to the x-axis, counterclockwise)", "End Angle")
'the new shape will be created on the currently active slide
Dim sl As Slide
Set sl = Application.ActiveWindow.View.Slide
'create the shape in the slide
Dim shp As Shape
Set shp = sl.Shapes.AddShape(msoShapePie, 0, 0, 50, 50)
'set the properties for Start and Finish angle to the values provided previously
.Adjustments.Item(2) = startAngle
.Adjustments.Item(1) = finishAngle
The shape is created at the top left of the current slide, and can be moved-resized from there (screenshots below).
The code may be different for other shape types (because of the different number and meaning of "adjustment" parameters), but the idea behind it remains the same.
Here are a few links if you need some help in understanding where to put the code/how to run it: