[Geometry]
Problem: The degree-measures of the interior angles of convex hexagon TIEBRK are all integers in arithmetic progression. Compute the least possible degree-measure of the smallest interior angle in hexagon TIEBRK.

Solution: The sum of the measures of the interior angles of a convex hexagon is $(6-2)\left(180^{\circ}\right)=720^{\circ}$. Let the measures of the angles be $a, a+d, \ldots, a+5 d$. This implies that $6 a+15 d=720 \rightarrow 2 a+5 d=240 \rightarrow 5 d=240-2 a$. Note that $a+5 d<180 \rightarrow 240-a<180 \rightarrow a>60$. By inspection, note that the least $a$ greater than 60 that produces an integer $d$ is $a=65 \rightarrow d=22$. Thus the least possible degree-measure of the smallest angle is $65^{\circ}$, and the hexagon has angles with degree-measures $65^{\circ}, 87^{\circ}, 109^{\circ}, 131^{\circ}, 153^{\circ}$, and $175^{\circ}$.

Final answer: 65