ABCDEF is a regular hexagon (I will sketch this in the session). Find the angle DAF

What do we know about hexagons? They have six angles and vertices. The fact that the hexagon is regular implies that all interior angles are the same. We can split the hexagon up into six triangles. These triangles are equilateral and hence each interior angle of each triangle is 60 degrees (180/3). Therefore x is clearly 60 degrees.

We can also do this knowing that each interior angle of the hexagon is therefore 120 degrees (Illustrated clearly with diagram). We have two regular trapezia formed by the line AD, so angles EDA and DAF are the same, and angles AFE and DEF are the same (which we have already established to be 120). A trapezium is a type of quadrilateral so the sum of interior angles is 360. So angle DAF = (360- 120-120)/2= 60 (which was our answer before).