Unfortunately, this is not so simple. You can set the circle object for which you specify the start and end angles. To cut out the center part, you should draw a second white circle above:
set xrange [-1:1] set yrange [-1:1] set size ratio -1 r1 = 0.5 r2 = 1 theta1 = -30 theta2 = 60 set angles degrees set style fill solid noborder set object circle at first 0,0 front size r2 arc [theta1:theta2] fillcolor lt 1 set object circle at first 0,0 front size r1 fillcolor rgb 'white' plot -10 notitle
It is important here that the x and y axes have the same unit ( set size ratio -1 ), since the circle object is defined in units of the first x axis and does not take into account the y axis at all. If you have nothing else to build, you should use the plot command, which displays something outside of certain ranges. Without a graph, objects are not drawn.
Result from 4.6.5:

In the next version 5.0, you can use pseudo-data (with a special file name + ) along with the filledcurves build filledcurves :
r1 = 0.5 r2 = 1.0 theta1 = 20 theta2 = 135 set polar set angles degrees set size ratio -1 unset raxis unset rtics set trange [theta1:theta2] set style fill solid noborder plot '+' using 1:(r1):(r2) with filledcurves notitle

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