SE-SKOLORNAS 2008 Problem 4

A convex $n$ -side polygon has angles $v_1,v_2,\dots,v_n$ (in degrees), where all $v_k$ ( $k = 1,2,\dots,n$ ) are positive integers divisible by $36$ . (a) Determine the largest $n$ for which this is possible. (b) Show that if $n>5$ , two of the sides of the $n$ -polygon must be parallel.