Hi, I'm new here.Often I have to make a closed polygon with curvy angles, for instance including part of a circle. I always make small straight lines to simulate a curve, but the result is not really good. Is there a trick to make curvy lines?thanks

You could try using the SPLINE command.You could use a series of connected polylines then fit a curve to them or a spline using the PEDIT command and the appropriate option either FIT or SPLINE.You could use the SKETCH command but be forewarned that this command uses a series of small lines (you control the length).  I've seen AutoCAD actually crash when someone got carried away using this command.  Use at your own peril.

The "trick" is learning how to create arcs within the basic polyline command.  In general, you need to work counter clockwise.  But depending on how complex your polygon is going to be you may also help yourself out by drawing a few guide lines for directions or angles, or even radii.
 
You could also draw your figure with basic lines and arcs and then convert that into a polyline after it's complete.  That might be the easiest route.  Sometimes trying to do something complicated with the polyline command can get out of hand in a hurry.
 
Dave.