We draw the circle and 18 radii to the points P1 to P18. Each of the 18 
central angles have a measure of  or 20° each.  



The angle P2P4P8 is an inscribed angle and it is measured by one-half
the arc which it intercepts.  That's the big red arc. There are 12 20° 
central angles subtending the big red arc (count them).

So the measure of the big red arc is 12*20° or 240°. P2P4P8 is the inscribed
angle subtending a 240° degree arc.  Since an inscribed angle is measured by 
one-half of its subtended arc, angle P2P4P8's measure is one-half of
240° or 120°
   
Edwin