### Instruction: Polygon $ABCDEF$ is a regular hexagon. What is the measure in degrees of angle $ABF$?### Response: To find the measure of angle $ABF$, I need to recall some facts about regular polygons and interior angles.
A regular polygon is one that has all sides equal and all angles equal.
A hexagon is a polygon with six sides.
The sum of the interior angles of any polygon with $n$ sides is given by the formula $(n-2) \times 180^\circ$.
For a hexagon, $n=6$, so the sum of the interior angles is $(6-2) \times 180^\circ = 720^\circ$.
Since all the angles of a regular hexagon are equal, I can divide the sum by 6 to find the measure of each angle.
That is, each angle of a regular hexagon measures $\frac{720^\circ}{6} = 120^\circ$.
Now I have the measure of angle $ABC$, which is $120^\circ$.
But I want to find the measure of angle $ABF$, which is adjacent to $ABC$.
How are these angles related?
I notice that the two angles form a straight line, so they must add up to $180^\circ$.
This means that angle $ABF$ is the supplement of angle $ABC$.
To find the supplement of an angle, I subtract it from $180^\circ$.