Triangles and Parallel Lines

In triangle ABC, angle A measures $60^{ ext{o}}$. A line segment DE is drawn such that points D and E are on sides AB and AC, respectively, and DE is parallel to side BC. The length of segment AB is 12 cm, and the length of segment AC is 9 cm. What is the measure of angle ADE?

Recall that when a line is drawn parallel to one side of a triangle, it creates similar triangles. Use this property to find the measure of angle ADE.