Polygon $ABCDEF$ is a regular hexagon. What is the measure in degrees of angle $ABF$?
An interior angle of a regular hexagon measures 120 degrees. And since $ABCDEF$ is a regular hexagon, all of its interior angles must measure 120 degrees. So, angle $ABF$ is an interior angle of triangle $ABF$. And the sum of the measures of the angles in a triangle is 180 degrees. Let $x$ be the measure of angle $ABF$. Therefore, $x+x+120=180$ And we can solve for $x$. $2x+120=180$ $2x=60$ $x=30$ The measure of angle $ABF$ is $30$ degrees.

