Hint for process of elimination: Go through each of the three statements individually and consider them for validity. Remember that the angles measure of a full circle is $latex 360\textdegree$. It also helps to know that supplementary angles two angles whose measures add to $latext 360\textdegree$.
Read on for a full solution.
Solution: Statement I says that the sum of all six angles is $latex 360 \textdegree $. The six angles complete a full circle, which adds up to $latex 360 \textdegree $.
Statement II says that all six angles are congruent, or equal. However, any three arbitrarily drawn lines that intersect at a common point do not have to make six angles that are a perfect $latex 60 \textdegree $.
Statement III says that any pair of adjacent angles is supplementary, or that their measures add up to $latex 180 \textdegree $. However, any straight line forms a $latex 180 \textdegree $ angle. In this diagram, any three adjacent angles form a straight, $latex 180 \textdegree $ angle, so the sum of the measures of any two adjacent angles fall short.