In the diagram, line a f is a side of regular hexagon abcdef inscribed in circle o. what is mfda?  

Since it is a regular hexagon, all 6 sides are the same length.  That means that the 6 vertices divide the circle into 6 equal arcs.  360/6 = 60° for each arc.  The arch between A and F is an intercepted arc for ∠FDA, and we know that inscribed angles are 1/2 of the measure of the intercepted arc. Since the arc measures 60°, that means that the angle would be 30°.