Problem 2 (1999 AIME)

Consider the parallelogram with vertices $(10, 45)$, $(10, 114)$, $(28, 153)$, and $(28, 84)$. A line through the origin cuts this figure into two congruent polygons. The slope of the line is $m/n$, where $m$ and $n$ are relatively prime positive integers. Find $m + n$.